Let me continue this train of thought even further. Your last sentence nails it. Even a firing for "performance" is not necessarily an indicator that the candidate before you would be a low performer
at your company.
Sometimes, people are fired for "performance," when what that really means is "new manager/tech lead didn't like them." Interview enough people and you'll see this at some point. Sometimes, low performers in one environment are star performers in another. This is what happens when founders are replaced by more experienced executives, among other scenarios. Sometimes, people with impressive credentials (PhD + significant publications + previous experience, for instance) will completely bomb your interview because they can't figure out which of their language of choice's container types is suitable to the task. I literally interviewed that candidate once. Sometimes, people are fired for straight up illegal reasons that have nothing to do with performance. (This literally happened to me at a big company you've probably all heard of and used their product.)
As a company and an interviewer, the best thing for all involved is for you to have a structured process with which to evaluate all candidates for a given position, and follow it. No interview process is perfect at either selecting good candidates or rejecting bad ones, but if you have and follow a structured process, at least you should get consistent results out of your interview process, and you can calibrate your hiring bar from there. I don't want to go into much more detail regarding "structured processes," but if you search on HN for u/tokenadult's hiring comment cum copypasta (albeit an informative copypasta), most of what's there still holds true according to the best and most current research on hiring.