"and the links all actually point to eBay" - most people who fall for these scams aren't sophisticated enough to know that the name in the link ("ebay.com") is not the same as the destination if you actually click on it ("giveyourmoneyawaytooffshorecrooks.edu"). This is why security experts say "don't do it" rather than "consider this factor, and consider that factor." If you want to protect yourself, don't do it. Don't click on the link, and don't "sign in" to respond to an inquiry.

eBay offers an option to send a message to an e-mail address, but it is always in addition to sending the message through eBay's message system. Therefore, if you receive an e-mail and you think it's legit:
(1) don't click on it
(2) open your web browser
(3) go to "www.ebay.com" - but don't click on a link in the e-mail to take you there
(4) sign in to eBay through your web browser (not through the e-mail)
(5) if the message is in your eBay messages folder, it is legit and you can answer it without signing in again.
(6) if the message is not in your eBay messages folder, it was a scam. You may congratulate yourself for refusing to fall for it.

Real e-mail addresses can be obtained through eBay through various methods. If you receive a real e-mail from a potential customer (an e-mail not sent through eBay's message system, but using an e-mail address obtained from eBay), you will be able to respond to it like any other e-mail. You will not have to sign on to eBay. If you receive an e-mail that tells you to sign in to respond, it - like the one Larry received - is a scam.