I try to remember to check the addresses and if they don't match, I contact them as to which is correct. I hate having to do this but I have had some instances where the Etsy address is correct and some where the PayPal address is correct. If you have to change to the Etsy address, you lose at least some part of the PayPal protection so I have added this to my shipping policies, "Also, if you want something shipped to an address other than your "ship to" address in PayPal, we will, if you add the insurance option." I seem to get a fair number of people buying as gifts and expecting me to ship directly to the recipient by giving me that address in the notes to seller instead of checking with me first or instead of changing the ship to address in PayPal. (some know how to do this thankfully)
I had a customer once that lived in Singapore, but had an address on the west coast that she wanted her purchases shipped to. Hopefully this is a similar situation.
Good luck. Situations like this are never any fun, but I believe that good customer service is important and unfortunately providing it sometimes feels like we are bending over backwards for someone else's mistake.
Some people put in their shop policies that they will always ship to the PayPal address if there is a discrepancy, but I think trying to be vigilant and contacting the buyer if there is a mismatch is the best way to handle a mismatch.