Problem with that proof is precisely what you've shown - those badges can be obtained independently and in themselves don't really prove the seller was actually in that position. The other things to consider is what that badge would indicate anyway - photo pass, stage hand, security team? Could mean they worked the venue that night and didn't get within 500 feet of Ariana. Also, aren't these people kind of not supposed to ask for autographs anyway? The whole thing kind of elicits more questions than answers.
That aside, I don't know enough about Ariana's signature to really make the call. But I wouldn't grab it on that "proof" alone.
thanks Rich. Common sense kicked in and I didn’t go for it in the end, but you’re absolutely right about that. It doesn’t look like her regular autograph but those are usually much neater