Let me elaborate. He won the auction of the item but wants to pay for the item not through eBay because his "app" on his mobile needs "updating" and won't let him finish the transaction on here.

A transaction conducted outside of eBay is where the item is listed here but is not sold here - for example a buyer contacts a seller and offers $X to a seller to end an auction and sell privately to them.

I wouldn't necessarily say their excuse is bogus, either, as there are quite a number of glitches with eBay mobile apps, particularly checkout ones, but in saying that if it was me I'd just go use a computer somewhere...

if it is still a paypal payment, won't the seller still be protected in the case of a fraudulent card or hijacked account?

As long as the item was sold on eBay and the OP receives a single payment via PayPal, they'll be eligible for seller protection if they have proof of shipping to the address.