After a quick look, it seems the two companies are indeed legally seperate(surprising), but the role of a parent company (controlling interest in another company) is still there, especially with their IPs. Miyamoto's demand for no story and Super Mario World characters only were made at the start of the Sticker Star project and required.

Except, now that I'm looking at my sources, the removal of the traditional experience point system to get away from the RPG style was an IS choice, mainly from Director Tanabe who started from Super Paper Mario. It seems the one mainly in fault for the series to move away from being an RPG is him, so it looks like you're mostly right in that Nintendo isn't the one responsible for most of the new changes to the series (still responsible for some of its direction though).