If there was an obligation to assign the patent, the assignee could take action to enforce the assignment against the will of an inventor. The obligation might arise indirectly if the inventor is obligated to A who is obligated to B.
One fairly interesting thing about the case is that generally in the US an obligation to assign arises out of a signed agreement. There are other contexts (e.g. government employees in the scope of their duties, maybe people hired specifically to invent) but for the most part if the parties do not agree the obligation does not exist. However, even with regards to the US patent, the relevant law governing obligations to assign might not be US law even if the case were heard by a US court.
I think there are procedures for allowing an assignee to record an assignment if he has proof of an obligation to assign and the inventor balks, but the recordation of the assignment with the PTO would not be the last word on the matter. The PTO stops way short of fully adjudicating the issue, and has no authority to determine the rights of the parties. The PTO is basically just deciding whether to record a document. The matter of ownership could be challenged at any time.
There is an interesting story involving a student named Taborsky who found himself in a dispute over patent rights with the University of South Florida. Despite having not signed any agreement to assign, Taborsky found himself jailed (for misappropriating trade secrets), subjected to deportation attempts by the state, and after repeatedly disobeying a judge's order to assign the patents, had the rights to a patent he'd been issued turned over to a company to whom the university had an obligation to assign. Some of the relevant facts of the case are subject to "interpretation" by the teller, but the case does provide an entertaining cautionary tale.