Note that this is all mostly speculation on my part based on what we know about the Monthly based Apple Care+ and what we discussed in your thread in the WC.
If you buy Monthly Apple Care+ it would need to be activated with your Apple ID is what I'm saying. 3rd party authorized retailers have access to Apple's systems and activate the regular warranty as well as Apple Care at the moment of purchase.
So if the monthly Apple based Apple Care+ option was bought at the same time you buy the iPad, it gets activated in the system on the Apple ID you provide to them.
However, if the monthly payments are done outside the Apple system, then its like buying a phone and financing it for 12 months or 18 months, interest free. You are technically buying the one time Apple Care+ , but spreading the payments over a longer period of time outside Apple's own system for it. This would not activate the Monthly Apple Care on Apple systems, and as such would not be manageable as a subscription.
Key point here, is if it had been activated as a monthly Apple Care+ subscription it cannot have been activated outside of the Apple ID and using its payment method.
The fact its using the Best Buy card, leads me to believe its not the actual Monthly Apple Care+ but the single purchase Apple Care+ spread into monthly payments on the Best Buy Card. In which case as you mentioned originally, they would need to go back to Best Buy to change the associated payment method with it.
Hope that makes sense.