If this is what you meant by conspiracy theory, I can understand your thinking (maybe). It seems to make sense in some ways too. You are basically saying that the NFL may have been complicit in:
a) wanting the Skins to change their name
b) trying to force more change from the Skins organization, potentially to include Dan Snyder leaving
Correct me if I'm wrong there.
#1 is easy to see, it was deemed "bad for business" and it became an easy call to make from their perspective. I understand that. Number 2, it sounds like you are proposing that as well. If the league wants to kick out an owner, they know they would have to look over their own shoulders a bit. Look at what happened to Cuban in the NBA when they had a big scandal involving harassment and mistreatment. He made big public amends and they eventually moved on (I don't remember other specifics, like penalties, but whatever the case, he has not come anywhere close to losing his team).
That is what I would expect to happen to Snyder in most scandal situations (and that is probably, in general, what owners PREFER to see happen without external interference). I can imagine that the NFL has a lot of owners who want Snyder gone, maybe not even as much for personal reasons as their number one motivation typically comes from pocketbooks, and Snyder is B-A-D for them there. I mean, you can spell that with CAPS. So, yeah, I'm sure they don't like him, but I also doubt they'd be eager to set precedents at a league level that they lose their independent authority. It's the same reason at the UN level, you always get certain countries who are saying "leave other countries totally alone" - not because they care about those other countries... but mainly because, they don't want anyone getting involved in THEIR national business.
When you examine the potential motivations and ramifications, I don't think it would totally add up. I can see them wanting Snyder gone, and not standing in the way of some bad rumblings that could force things to move (although again, if it hurts the brand, even there they may try to limit the exposure), but that falls well short of a big conspiracy. I don't see an extremely active hand being likely, because to me it would seem like it would run counter to their own selfish interests. Even on the grounds of being poorly run, you'd get other poorly run franchises worrying that the league would come for THEM next.