The ORIGINAL version of MAME, before MANY different coders' "projects" were merged, originally played Galaxian and the PAC games. It ran in pure DOS mode and was released in 1995, if my memory serves me correctly. That is WAAAY before ANY of the in-1 boards were conceived. Back then, memory chips big enough to hold the ROM images for multiple game images were way too expensive to make them viable for production. Also, a custom processor capable of emulating the Z80 and other CPU's used in "classics" was not available, or at least was not feasible either at that time. The first in-1 boards came out at least 10 years later.
I personally don't think that the in-1's use MAME simply due to the fact that all of the various issues (like sound problems) do not exist in MAME. If it were, then the sound issue (wrong sounds or missing completely) COULD be the result of a hardware issue, but I don't think that is likely. I think that they don't even REALIZE that there are problems because they don't even have access to the original boards/hardware. How else would you explain the obnoxious static noise that happens when you die in either Galaxian, Scramble or Super Cobra in BOTH the 39-in-1 AND 60-in-1 models? To make matters worse, when the 60-in-1 boards were released (and I suspect even to this day), the "fire/shot" sound that was present in the 39-in-1 version of Galaxian was COMPLETELY MISSING from the "new" 60-in-1. Again, if it were MAME based, I don't think these issue would be there...