Are people really going to confuse a frequent flyer program and a payment system?

Perhaps not right now, but Google has already shown their interest in the flight information industry with their pending $700 million bid for ITA. Its not a stretch to assume that they may use this acquisition to provide a method to search-for and purchase airline tickets using their mobile payment system.

I'm sure, if this is going to court, they will have some money in the bank to pay them.

but is it worth it?

I don't know, but it's like the Apple + Cisco thing about the iPhone name.