It's because those concessionary rates for home fans are based on having a membership (said prices in brackets on their price list) - that's what I was told when I queried right back when the first ticket news piece came out.
If a home fan who was a student/17-19 doesn't have a membership, they are charged the full whack.
I didn't believe the person who told me, but they were adamant and if you try and book in the stand along the side of the goal on their ticketing site, it only offers you Adult/12-16 and U11, so it does match what I was told.
In terms of 60/65 differences, this is something I've noticed a few grounds, even with similar facilities offered. Always been some getaround clause.