YIKES! I wonder if he is getting copies of your emails as well?
Have you tried sending that person an email from outside of Paypal. It may be worth your while to do that and see if you get a copy of it as well on your inbox. If you don't then it's definitely a PayPal issue. you may want to send them a message telling them that you are receiving all their PayPal related emails or something like "this is a test", from your own email client. After it is sent, check to see if you get a copy of your own email in your inbox. If you do, that's a GMail issue, If you don't, then it's a highly suspect PayPal issue.
I would also assume that this person is also receiving copies of your PayPal related emails as well. In any case, PayPal customer service should be notified about this ASAP. It would appear that those emails are going to both of you, kind of like a CC type of thing. Serious breach of personal security if that is the case.
P.S., check your account settings for attached email addresses, make sure that the other version is not present, if it is, delete only that one. If it isn't, contact PayPal customer support as quickly as possible as the only way to get rid of that other email would be to get rid of your own. (I suspect.... But they could tell you for sure.)
