I had exactly the same thing happen to my account about 6 months ago. I really freaked me out at the time too because I don't use a guessable password either.
I went through the eBay live help with no problems - lady there was fast and helpful but would not go into specifics as to how my account was hacked - she just gave me a standard reply like the one in your first post. The eBay notification I got did say that they sent out emails to spammed people explaining that my account was compromised.
The only thing I could think of was a key-logger but everything else is fine - hotmail, gmail, home email, amazon, bank accounts, PayPal - I mean surely they would rather have my bank account or PayPal details than eBay.
Six months later everything is fine, so I've basically concluded that there's probably a hole in eBay security somewhere that a bot managed to get into.