No is not an answer
If you are already booked, or if you don't play that kind of gig, no matter what, the answer is always, "Thank you so much for getting in touch with me. I would love to refer you to my good friend, the splendid pianist, so-and-so."
Never tell them their gig isn't what you do! You might change your mind later, or you might study hard and become brilliant at it. Or maybe you'll never do it, but meanwhile you can use the opportunity to refer a friend who fits better and could use the work. Keep musicians working! You're part of the community. Yes, you compete, but you can be a colleague, too.
Now my dinner theater job wasn't exactly a plum job, but it was respectable, steady work and it made me a MIDI expert. I used it as a networking opportunity. If I took off a show, I called all the best Broadway players who already had jobs. I once even called the original conductor of Annie. I knew they were all already working and none would be available to come do a dinner theater gig for one night, but they referred me to others who were and moreover they came to know me as somebody with something to offer instead of someone with something to take. I got tons of referrals in turn and spent a decade living mostly on the road with Broadway shows. It was fabulous.
Back to the Pierre
Another young jazz pianist friend responded to me on Facebook Messenger within minutes. I made the referral to the event planner and not only did my pal get the gig, he upsold the event planner his trio, creating work for his two sidemen, too. How smart, savvy, and cool is that?
Of pagers and smart phones
I remember when I got my first answering machine. Then I got one you could call into to retrieve messages. In the 90s, I got a pager. Always the hacker, I rigged my answering machine to page me the very moment anyone left a message. I never missed a gig call. When someone is hiring, they go down the list until someone picks up, just like I was doing for this Pierre job.
The old-school guy with Grammies didn't win the Pierre. The kid with a smart phone and Facebook Messenger did. I think that is so cool, and it is another lesson to add as a postscript to this story.
The fastest connection wins.