Having some MHP3 monsters doesn't mean "it's also based on MHP3". They're two different games. MH3G is based on MH3. It has monsters from other entries as well, but it's not based on them.
I was just wondering about the relationship between MHP3rd and TriG because i had seen people referring to TriG as being the 3rd release of the game. From what i gathered of the previous replies in this thread, seeing that TriG is not a brand new game, i understand that it has stuff (or being based on) from MH3 and MHP3rd, and then some new stuff is added as well. So TriG has stuff from the most popular MH game in it as well. That was the thing i was wondering about =)
EDIT: I added some text.