'National' and 'Museum' are doing the heavy lifting here to make you feel this way. Its a privately owned collection incorporated as a non profit to avoid taxes.
It's a cheap way to get a veneer of respectability. The best example of this I know of is the "National" leprechaun museum. https://www.leprechaunmuseum.ie/ . At least they had the good taste not to put it in the domain name.
Is this possible? Their own website says “With your generous support we have expanded the list of motorcycles on display from 40 to over 500.” If that means many of these were donated, it doesn’t seem to be a private collection.
Maybe the non-profit is the museum without the collection, and the museum just shows non-museum owned stuff?