The longer you're playing, the more likely it is you've got JTR, thus also a more developed roster. On a guild level, i think it's safe to assume that guilds with loads of JTRs also have loads of developed rosters, even the players in that guild that didn't yet unlock JTR.
I don't think anyone in my guild has ever used a different team for p1 heroic than a JTR team. So yes, you pretty much "need" an x amount of JTR teams to be able to clear the raid. Maybe you can also clear p1 with different teams, but it's wildly inefficient.
It is indeed not as punishing to use other teams than chexmix in p3 as it is as using other teams in p1, not by a long shot. Just don't underestimate how many additional. well geared teams it's going to take if you want to clear that phase with just 5 or 10 chexmix teams for example.
However, the point i was trying to make is that it's probably not the lack of JTR teams that is preventing guilds from clearing the HSR. I'm sure there are some cases where it is in fact the lack of JTR, but those are probably very rare. I'm convinced there are loads of guilds out there that have enough JTR teams to potentially clear p1, but won't come close to clearing the raid.
In conclusion; if your guild has 20 or more JTR's, she's definately NOT the reason why you're not able to clear the HSR. So if that's the case you'd better start looking for a different scapegoat.