Minchas Shai there quotes various versions which were changed in order to answer your other question about style of the surrounded Pesukim, but seems to agree that there were not many old manuscripts that contained this (he does note that some old printings have these additions).
Daat Mikra also notes that they were copied into some Sefarim, but defers to Minchas Shai's analysis, which he quotes in a footnote. Both seem to agree to Radak that there are no accurate manuscripts with this "error".
Daat Mikra also notes that the source of this error seems to have been the Septuagint here (Yehoshua 21:36), which quotes these verses (originally from Divrei Hayamim I 6:63/64) here, however, they were likely included as an explanation of the remaining cities (the Passuk says 12 cities, and only lists 8).
I now see that I cannot do a better job than this extremely thorough answer on Biblical Hermeneutics, which is a duplicate of this question...
Edit: However, I will add this quote from the Pulpit Commentary (Yehoshua 21:36), which defends the added text, and provides a reason for its omission (the "arba" ending), as well as a list of commentaries that defended it:
Verse 36. - And out of the tribe of Reuben. This verse and the succeeding have the Masoretic note appended that they are not found in the Masora or true tradition. Kimchi therefore rejects them. But they are found in the LXX. and the rest of the ancient versions, and they are necessary to make up the number of forty-eight cities. Dr. Kennicott, as well as Michaelis, Rosenmuller, and Maurer defended their genuineness. So does Knobel, who complains that Rabbi Jacob Ben Chajim, in his Rabbinical Bible of 1525, has very improperly omitted these towns on the authority of the Masora, and that many editors have foolishly imitated him They have no doubt been omitted by the mistake of a copyist, who passed on from the אַרְבָע (four) of ver. 35 to that of ver. 37, omitting all that lay between. The LXX. adds here "the city of refuge for the slayer," words which may have possibly formed part of the original text, as they do in every other instance.