I said I couldn't imagine them doing it manually, not that they didn't know how. The incentive simply isn't there. If it was important to them, they could have done a database check at the time of booking.
The reason the incentive isn't there is they wouldn't be getting back thousands of dollars. The offer's T&C's say, " If Disney+ subscription cannot be verified, reservation will be cancelled with applicable fees." In other words, this wouldn't be money in Disney's pocket, it would be a lost booking/lost revenue. With these sailings going on now or in the coming weeks, still having availability, canceling bookings is not a win for Disney.
This promotion was nothing more than a way for Disney to fill ships without admitting bookings were very low for those months. Instead, they look like the good guys for giving such a generous promotion to loyal customers, and get a positive promotion for another company product.
Like I said, it is just a hunch. I'll change my mind when we see the first person post here or in a Facebook group that their $5,000 booking was canceled because they weren't paying $6.99 a month to Disney.