Maybe one pressing of Past Masters had the wrong version.

He probably could tell which version he played drums on if he heard them. I was referring to an interview where he said Andy White's drumming was the original single and his drumming was on the Please Please Me album. Of course the reverse is true.

I don't think so. There's no tambourine on either the Please Please Me version or the Beatles' Hits EP version. The version on Past Masters, billed as the original single, has the tambourine.

No, it's the opposite,
both the EP and the album have the tambourine version with Andy White on drums while Past Masters has the Ringo on drums version, sans tambourine.

Not on the versions I've got!

They must not be official releases, maybe bootlegs. Here's the Past Masters version with no tambourine.

I bought The Beatles' Hits from my local record shop in February 1964, a few months after it was released. At the time I had no idea there were two versions of Love Me Do. When I did find out I asked two Beatles experts (separately) and they confirmed the bad news that the EP version I had (without tambourine) was the LP version. I was given the LP (possibly the last vinyl pressing!) in around 1994 - my brother bought it from his local record shop. Again, no tambourine.

We all know there have been mistakes down the years - maybe one pressing of Past Masters had the wrong version. For my part, I'm glad to have both versions, so I know I've got the hit single!