The short of it is that there is a gemara which says that tekef le-netilas yadayim beracha. And while everyone nowadays assumes this refers (or refers as well) to mayim rishonim and the beracha of hamotzi, classically beracha refers to birkat hamazon, and so it is clear from the way the gemara uses the statement in context. And so pasken the Rambam and Rif, but the Rosh was noheg this for mayim rishonim as well, and the Tur brings this down as the halacha. There is, after all, a Yerushalmi which speaks of three tekefs, with this as one of the three, and it assures that if one does this, the Satan will not be mekatreg in all that seudah, which might imply that it is before the meal, such that the reference is to mayim rishonim. Also, I would add, there is another gemara in masechet berachot, where a fourth tekef is used, that tekef le-netilas yadayim seudah (and see Tosafot), as one of two possible answers of preferring either Bet Shammai or Bet Hillel, where we might indeed consider this as something of value. But this has to be the short of it, because that is not the focus of this post. (All this from memory, so I hope I didn't mess anything up.)
I have another post in the works about the Maharshal's teshuva (34), where he explicitly opposes this requirement set by the Tur.
But the other day, JNUL scanned Rabbenu Bachya ben Asher's Shulchan Arba, where he discusses the gemara and the requirement imposed by it. Rabbenu Bachya ben Asher was just about contemporary to the Rosh.
As you can see, he cites the requirement of tekef le-netilas yadayim beracha and explains it ke-peshuto as that one who washes his hands for mayim acharonim, he should bless birkat hamazon immediately. And that we find the same in the Yerushalmi. Then he cites the Yerushalmi, and does not indicate in any fashion that he believes the Yerushalmi is referring to mayim rishonim instead.
A useful data point.