Why recite the fourth Berachah of Bentching in a case of doubt?

Question

If someone is in doubt whether or not to Bentch, we take the strict approach and require the person to Bentch, as it is a Biblical requirement (see here), unlike most Berachoth, for which the rule is not to recite a potentially unnecessary Berachah.

Although the fourth Berachah is not considered Biblical, the Mishnah Berurah (184:4, s"k 13), based on the Magen Avraham, says we don't want to treat Bentching disrespectfully, so we should recite the fourth Berachah as part of the whole.

Is this widely accepted, and what is the basis for this ruling? (I saw the citations in the Sha'ar HaTziun and looked up the Magen Avraham; it seems to me that it is a Da'ath Yahid following a Da'ath Yahid, but maybe I'm mistaken).

Answer 1

Shulchan Aruch Harav also says the same thing, and adds a second reason.

וכל מקום שחור ומברך צריך לאמר ג"כ ברכה רביעית שהיא מדברי סופרים כדי שלא יבואו לזלזל בה, ועוד שכך היתה התקנה שבכל פעם שמברך ברכת המזון יברך ד' ברכותה

The first reason I understand him to be saying not that you would treat Benching as a whole disrespectfully, but that you would treat the fourth blessing disrespectfully, and perhaps not take it as seriously in other contexts.

The second reason is that the Takanna of benching was all four Brochos, so whenever you Bench you say all four. I think that means that the Rabbinic requirement in this case is to always say all four together, even in a case of doubt (thus being the Rabbis made an intentional exception to the rule in this case).

Sources for both those reasons (in addition to the Magen Avraham) are in the footnotes at the link.