Some bentchers include the pasuk 'poseach es yadecha..." at the end of the first paragraph of bentching (before the closing bracha), while others do not. What is the correct girsa? Are there different minhagim?
Kolbo (quoted by Beis Yosef 387) says not to say פותח את ידך for how could we bring a verse Dovid Hamelech said with the words of Moshe Rabeynu. However the Beis Yosef himself rebuts his reasoning (without explanation). The Ram"a in Darchei Moshe there says the custom is not to say it.
According to the Mabi"t (Sha'ar Hayesodos Perek 61) these words actually originated in Birkas Hamzon, and were later adapted into Tehillim by Dovid Hamelech. The Brisker Rov (quoted in Simchas Yavetz pg. 137) explains that therefore we say "כאמור" ("as it says") and not "ככתוב" ("as it is written"), as we do in the second blessing - since it was not yet written.
[However others (see Kesef Mishna to Hilchos Brachos 2:1) explain that this that it says in Brochos 48b that Moshe established the first blessing of Birkas Hamazon refers to just the general enactment and not the specific words].
I once read in an Artscroll Birchat HaMazon (the one from the 70s with tons of commentary on the bottom) a discussion that went something like this:
Moshe Rabbeinu composed the first paragraph of Birchat HaMazon (Berachot 48B). As such, his version obviously did not have the line "As it is stated, You Open your hands...." (since David HaMelech hadn't written it yet).
However, the prayers we have today are the ones established by the Men of The Great Assmebly. When they finalized the nusach of the Birchat HaMazon, they added the one line to Moshe Rabbeinu's prayer.
Perhaps this is according to the opinion that adds the line to the Birchat HaMazon, while the version that does not add it is of the opinion that the Men of the Great Assembly did not add it to the prayer when finalizing it.