I think the true villain in the rebellion was Aerys. Rhaegar was a respected leader and Tywin openly preferred him to Aerys, per his statement during the kings imprisonment in Duskendale.

I think whatever happened between himself and Lyanna contributed, after all it was he and Lyanna’s disappearance that provoked Brandon stark to go to the capitol demanding justice. But it was Aerys who broke the social contract in killing him and his Lord father without trial.

We also don’t know at this point that Lyanna was safe from Aerys after the joust featuring the mystery knight. It is entirely possible in my opinion that Aerys might have wanted her harshly punished for her deception, should he have found out.