Like today, it's pretty easy to survey study and review abstracts and even browse certain articles online. It wouldn't be alien for George Costanza to have access to a medical journal today. But I have no idea what public access to medical journals was like back then. In the context of the show, it is clearly a lie because George is just a huge liar. But I'm curious if audiences back then could have imagined some way George Costanza was going around reading medical journals or even if they knew what medical journals were like.
Any university library and most larger city libraries would have medical journals available. Even my county library still gets four paper copies of JAMA, but the more specialized journals have switched to electronic.
George lived at 1344 Queens Boulevard. There is a branch of the Queens Library about six blocks away, and they get the paper JAMA at least up through 2011.
Tom's Diner was just two blocks from the Butler Library at Columbia University, although you might have to go another 40 blocks to the medical center to get the really good Nephrology Journals.
George's character is a noted hypochondriac. Plowing through journals is not light reading but George tended to put a lot of effort into the wrong things.