The Catholics weren't offered a choice. The entire church organisation, with all its buildings & other property, was snatched out from under the pope, and most of the clergy (including those in charge of York Minster, headed by the dean, & the archbishop at the time) went with it, so it's hard to see who the Catholics were who might have been reluctant to hand it over.
Just one of those little impossible stories made up to 'explain' something which already had a perfectly good (& true) explanation, like a lot of folk etymology.