I'm not speaking for any entity - just as someone that's done a LOT of IP work...

If the results are published prior to the IP protection without appropriate non-disclosure in place, then the work becomes unprotectable. That's referred to as Prior Art or the Process of Display.

They may own the work but if they publish prior to protecting their priority dates, they lose all priority.

I'm operating under the assumption that anything I contribute to the project will be done with as the Regents of Mt. Sinai and their Board see fit. That it is a gift of services rendered with no potential return to me, and no possibility of practical return.

I think the faq is pretty clear on that. I'd be willing to bet my last dollar that any international court would read that as appropriate disclosure and with the intent being as I wrote above... YMMV