I haven't been watching this cartoon, so I don't know the specifics of what happened. However, the "gravity wells pull you out of hyperspace" thing isn't contradictory to what Han said in a A New Hope-----recall that his next words were, "and that'd end your trip real quick, wouldn't it?" Which implies that you wouldn't really pass through the star, you'd get burned up inside it. And one way that could happen is if you get bumped out of hyperspace such that the combination of inertia and gravity make it difficult, or impossible, to pull away from the star.
This was certainly the assumption that Timothy Zahn was writing under in the Thrawn trilogy. However, if you need an excuse to make it possible, you can always come up with one. For instance, here are two right off: (1) Expensive models of hyperdrive are capable of getting further into gravity wells than the cheap ones, or (2) Flying in a gravity well is dangerous, but not impossible; the hyperdrive kicking you out near one is a safety feature than can, on some models, be disabled.