This question and answer uses the full amount of the mezonos eaten as the basis for the answer. This would also seem to apply, though you should ask the rabbi involved. Note that this also leads to the question if seudah shlishis requires a kevias seudah or not, something that should probably be a separate question. The practice cited in your question, implies that this rabbi says not, but that is a different issue.
Mezonot Rolls Rabbi Ari Shvat
What is the status of mezonot rolls? I have seen very conflicting
opinions - some stating that they are a halachic fallacy and others
saying that the concept works (most notably on airplanes). Can this
opinion be relied upon even when you are having a meal with a mezonot
roll (kovea seudah)?
You're right, there are different opinions regarding
"mezonot rolls". For sfaradim it's simple, for the Shulchan Aruch (Or.
Ch. 168, 7) holds that as soon as the fruit juice is tasted in the
roll (which I imagine is the case), its bracha is mezonot and doesn't
need washing or benching. For Ashkenazim, the Rama writes that it's
mezonot unless there is so much honey or spices that it's almost the
ikar (the main ingredient). The basic understanding would indicate
that those rolls which taste like rolls more than they taste like
cake, are hamotzi, and accordingly, there's no such thing as mezonot
rolls. On the other hand, others (Chabad, Maharsham) say that
according to th Rama, it's enough for the amount of fruit juice to be
more than the amount water in the batter. This does not set well with
the wording of the Rama and therefore is better not to rely upon. On
planes or when it's difficult to wash, there is on whom to rely,
nevertheless this is less preferable. Kviat Seuda on mezonot is when
eating about 4 k'beitzim, about 8 slices of bread (some say even
more), something which isn't that common, so that hardly comes into
play here, even according to the lenient opinion.
With Love of Israel,
Rav Ari Shvat
There are those who defend the use of Mezonot rolls on a number of different issues. Rabbi Ari Enkin a resident of Ramat Beit Shemesh, is a researcher and writer of contemporary halachic issues. He is the author of the “Dalet Amot of Halacha” series (8 volumes), Rabbinic Director of United with Israel and a RA"M at a number of yeshivot. www.rabbienkin.com posted an article with an explicit caveat. As a result, you should speak to the Rav involved to understand how he approaches this issue. Note that this article also cites the kevias seudah definition.
The above is intended to serve as a “limud zechut” only. It remains the opinion of this writer that Ashkenazim should always consider
mezonot rolls to be like any other bread requiring netilat yadayim,
hamotzi, and birkat hamazon, regardless of any other considerations.
His first point is that there is indeed a difference between sefardim and ashkenazim. Additionally, since your question involves seudah shlishis, which would seem to be kvias seudah, the issue would be more complicated than the plain usage.
In Defense of Mezonot Rolls
The main difference between bread dough (“hamotzi”) and cake dough
(“mezonot”) is that the latter is sweeter and enjoyed far more often
as a snack rather than as a meal. According to the Mechaber, as long
as the sweetness of the dough is merely discernable it is sufficient
to render the product a “mezonot” item. According to the Rema and
most other Ashkenazi authorities, however, the sweet taste has to be
the most dominant feature of the product.
The opinion the Mechaber is unequivocal. Therefore, with the exception
of the issue of “keviat seuda” which will be discussed below, Sefardim
and others who follow the rulings of the Mechaber are certainly
entitled to enjoy the convenience that mezonot rolls have to offer. It
is unclear, however, upon exactly what basis Ashkenazim who use
mezonot rolls rely.
There are those who interpret the ruling of the Rema in a manner which
would allow bread to be declared “mezonot” as long as the liquid
component of the dough consists of more fruit juice than water.
This is true even if one does not taste the fruit juice in the
 OC 168:7
 Rema, OC 168:7.
 Daat Torah 168:7, Shulchan Aruch Harav, OC 168:7.
 See Shevet Halevi 8:32, 9:44 for more on this.
However as mentioned in your question and in the cited article, kvias seudah is a more complicated matter. It appears according to the cited article below, that the mezonot rolls may be used as a result of the amount of food actually consumed at the seudah shlishit. This would imply that the situation that you are referring to may be regarded as not kvias seudah. This would depend on the actual situation there and if seudah shlishis requires a kevias seudah or not.
There is, however, another issue which must be dealt with before
mezonot rolls can be comfortably consumed, and that is the issue of
“keviat seuda“, establishing a meal. According to the principles of
keviat seuda, one is required to perform netilat yadayim and recite
birkat hamazon when eating a quantity of mezonot items (“pat haba
b’kisnin”) that one would consume if such items were in place of a
meal. However, there are many different interpretations as to what is
defined as “a quantity” and “a meal”.
According to the most lenient interpretation of keviat seuda, only one
who eats an amount of mezonot products which is equal to the quantity
of bread one would eat at a normal meal is required to perform netilat
yadayim and recite birkat hamazon. Eating an amount of mezonot
products less than this will allow for one to simply recite “mezonot”
and “al hamichya” according to this approach. Such conduct is even
better justified if the mezonot products are not eaten together with
any meal-type foods. Therefore, one who is served an airline meal
which contains a mezonot roll should eat the mezonot roll separately,
with its own bracha rishona and achrona, and only then proceed to eat
the other foods which are served along with it.
Eating mezonot rolls together with meal-type foods is slightly more
complicated due to the principles of keviat seuda, the details of
which are beyond the scope of this paper. With regards to the common
mezonot roll sandwich, the mezonot roll is already packaged and served
with the “meal-type” food, as a sandwich should be. Removing these
items (tuna, egg, salami?) in order to eat them separately from the
roll as advised above is usually impractical and unappetizing.
Therefore, it is preferable for one who is going to eat a mezonot roll
sandwich (or pizza for that matter) to eat less than the total
quantity of food that is normally consumed at a meal in order to
better justify reciting “mezonot” on such sandwiches. However,
according to the lenient interpretation of keviat seuda cited above,
as long as one eats less than the total quantity of bread that is
normally consumed at a meal, there will still be some justification
for the use of mezonot rolls along with other foods as a bread
 Aruch Hashulchan, OC 168:17; Shulchan Aruch Harav, OC 168:8; Kaf
Hachaim, OC 168:47; Igrot Moshe, OC 3:32;Yabia Omer 8:22:21. For more
on this see Vezot Habracha p. 28-36 and p. 219-226.
 Mishna Berura 168:24. See also Shemirat Shabbat K’hilchata 54 note
132 and Vezot Habracha p. 32.
 Az Nidberu 5:33; Mishneh Halachot 7:26.
 Shevet Halevi 8:32.