George Hamilton is not confused.
The interview featured with George is actually from a Las Vegas TV interview with Rona Barrett in 1969, so his statements are correct. It is not known, as far as I recall, if the interview is from the actual opening night, or another date. Like a lot of things in This Is Elvis, some poetic licence was taken with editing, hence a 1969 interview used with 1970 footage to showcase a 1969 comeback.
The two or three seconds of George featured in Way It Is (SE) may well have been taken August 10th - his hair is clearly longer than in the interview, and he is wearing a different suit and tie.
George attended both July 31st, 1969 and August 10th, 1970 along with many other shows.