Something to keep in mind is that sometimes a pool will be paid directly to include a transaction with a small fee.
From what I've seen, that fee is not "small":
English is hard.
Let's try that again, but I'll make an effort to be a bit more clear in what I'm saying...
Something to keep in mind is that sometimes when someone sends a transaction with a small transaction fee, they may later choose to make a completely separate payment to a pool to incentivize that pool to include that low-fee transaction in one of their blocks. That separate payment might be made with a completely separate bitcoin transaction, in which case it may show up in the same block as the low-fee transaction or it may show up in an earlier (or later) block. That separate payment might also be paid via a completely different method, such as Lightning Network, an altcoin, physical cash in local currency, or local currency electronic payment (ACH, SWIFT, Wire, Venmo, etc).