> But if TPG is an agent of the customer, then AA should be suing the customer.
Respondeat superior lets you sue the principal for torts of an agent committed in the scope of their agency, but it doesn't eliminate the liability of the agent for their own torts.
You typically want to sue the principal when the agent is less able to pay, less willing to settle, or one of many easily replaceable agents employed by the principal for the same purpose.
When the first and third of those are reversed and the second is unclear (which seems to be the case here), you want to focus on the agent. You could sue the multitude of principals, too, but that's just a lot more cost for little additional benefit (and possibly sympathy backfire in a jury trial.)