Signing a power of attorney for bank when selling your RV

Does seem strange. Assuming SE Financial is a legit bank, if you don't want to tank the deal right away, you could always "inquire" about the process at another branch and see if they give you the same story.
Might be someone doesn't know what they are doing, might be a real policy although I've sold items that the buyer was taking a loan and never have encountered that.

I can say with certainty, there are sometimes corporate processes that we don't understand, but may be ok.