So how is it in the US - do such payments require a legal bill issue through a registered company or are you allowed to pay such things in cash up front, no bills, no record? How do you deal with income taxes?
It really just depends. For small gigs paying a few hundred dollars to the band it isn't uncommon to get paid in cash. Many venues do insist on paying with a check though and they will make it out to a single person (the BL presumably) who will receive a tax form from the venue and be responsible for paying the taxes at the end of the year. The BL will then issue a 1099 tax form to the band members to account for the money they received.
It's a little more complicated than that with meeting taxable thresholds and whatnot but that's the very general jist of how it works here.
As to the OP's situation if I was the BL I'd give it back and just eat the $100, it's a small amount of money not worth losing a gig over. I would not put myself in the position of asking for money back from the band members.