This is the correct grid- the last one had a mistake- apologies!

Glad All Over was never recorded by the Beatles. Memphis, Tennessee was part of the Beatles stage act, but the only recordings are from radio broadcasts so its a bit of a stretch to call it a Beatles song.

I used a list from a website at https://www.beatlesbible.com/songs/
I'm not an aficionado- I can only trust the facts on the internet, such as they are. You may be right, the site may be wrong?
The criteria for the groups were as listed- the Beatles related element said "recorded by" rather than "written by, Beatles songs or original" etc.
These Criteria were a limitation on me more than on the player- they fit the set criteria of all being from the list- you didn't really need to put the Beatles bit to get a point, it just makes the grid more interesting (at least to me, certainly setting it) to have one great, whole grid false group. I only included it in the answer/ scoring out of fairness and so people don't get frustrated.

This was from another source (wiki):
The Beatles recorded "Glad All Over" on two occasions in 1963 for BBC radio sessions, with George Harrison on lead vocals. The first of these, recorded on July 16, 1963, was released in 1994 on Live at the BBC.[5]

On November 11, 2013, a second version recorded by The Beatles for the BBC Saturday Club radio program on July 30, 1963 appeared on the On Air – Live at the BBC Volume 2 collection.[6]

also found one that said they recorded Memphis, Tenessee five times