Everything worked correctly here.
The bid was:
$1250
then you bid $1301.02 and eBay moved you to the high bidder, with your bid being 1 increment above the 1250, which is $1275. So there you sat, the winner at $1275. For 1 second you were the winner. Then the other bid came in they bid more than you. By at least an increment. They don't have to beat you by an increment. They only have to outbid you by one to have their bid placed. That's the way eBay works.
Thus their max bid was truely $1305. Otherwise eBay would have forced their bid to be an increment higher than yours which would have been $1326.02. That's how I can tell that the winners true max was $1305.
In short, you don't have to win by a bid increment, you only have to bid an increment higher to have your bid placed. that means if you bid say an increment + 1 cent more, you can possibly win by 1 cent even if your bid comes last. As long as your bid is higher than the other persons.
eBay worked correctly, and AuctionSniper worked correctly. No blame to anyone. It's a tricky one. The step eBay doesn't show is where you were temporarily the high bidder at $1275. I'm not sure if they used to do that and stopped or what.
I doubt the eBay reps know that other bidders max was $1326. That makes no sense if the winner won for $1305. You should tell them that the buyer told you their max was $1776 and I bet they change their story and start telling you the bidders max was $1776. Why would they disclose another customers max bid to you? That doesn't seem right.