I have run into this several times. Usually in other cities where they have local bands opening the show. Now, with all humility, I tend to use pretty monster rigs (ie Ampeg SVT-7Pro / SVT-810e, Genz Benz STLMX 12.0 / 2 X UB410-t etc) and I dont let anyone else use my rig unless I know them personally and know that they understand how to use it properly....
Two pretty good examples stand to mind:
Last week we played a medium size venue with a National Touring package including DIRGE WITHIN and KITTIE.... The whole tour were awesome guys and we had a great time travelling with them. So we showed up at this venue and the promoter had scheduled 3 local openers... not at all out of the ordinary. The one band looked very young and it was clear that all of their parents and grandparents were there. A couple of the kids approached me and told us they like our new album etc.. smalltalk etc... and then the one kid says:
"So hey man, I need to use your rig tonight. Cool?"
I was kinda taken aback.... mainly because it was posed as more of a blank statement than a question... I said that I was sorry but I dont let anyone use my rig. He immediately got snotty and said that anyone who was "cool" would let him use a rig and what the F*** was the problem.... Now bear in mind... we're on the edge of fighting words coming from a 5'2" 14 year old... I'm no toughguy but this kid was pretty bold.... I told him hey... we're here to play and we dont want to cause trouble, but I just dont let anyone use my rig.... Then, like OP's situation, he started complaining that this is his first big show and it's being ruined because I wont let him use my rig.... I told him that HE ruined his gig by not arranging for his own rig.... and that he caused his own problems. Later, I went inside to check the band out and sure enough... the kid had his own "rig" the whole time, an older Peavey combo amp.... he just wanted to use mine.... And as soon as this middle school band was done playing, they and all their mommies took off immediately and didn't stay to support the other bands. Disgusting.
A worse example was a few years ago when I was on a major tour and we were playing this gigantic Skate Park in Buffalo, NY. The Promoter had set up one of these all-day affairs with like a dozen locals.... which can sometimes be cool but is more often a logistical nightmare. At the time, I was using a very complicated component rig with a two different preamps, a stereo compressor, power amp and a couple of signal processors. Again, some obnoxious little snot from one of the local bands struts up and asks to use my rig. I asked him why he was playing a sold out show in front of like 2,000 people without a rig, and why not just run direct to the PA? Again, I was educated on how "uncool" I was being....and I managed to fend the kid off. Later, I saw that he had actually gotten someone, or more likley several someones, to lend him gear. He was up on stage with a Sansamp BDDI, with every knob literally dimed, a chorus pedal.... again with every knob turned all the way up, An SVT-4Pro with, you guess it, every knob and slider turned all the way up, all plugged into a GK 410. Obviously the kid was a complete tool, and as I'm watching him hammer away at his beat up ibanez (with a quarter, not a pick), I see what looks like bright lights flashing inside his borrowed GK cab. Many cabinets have a small bulb on the internal crossover to soak up excess wattage... and this kid was taxing it to the max. I couldn't suppress a little laugh as the light stopped flashing.... and shortly after smoke.... thick black smoke started blowing out the ports.... let me tell you boys and girls..... there is nothing so "Metal" as the sight of flapping speaker cones backlit by flames from a melting crossover. Soon, there was literally flames licking out of the ports, and they had to stop the show to put the fire out..... Toolbox bass player thought this was awesome.... being that it wasn't his gear. Later while we were loading out, I overheard the heated argument between toolbox and the cabinet's owner.... tool is screaming that the owner's cab was a POS and that's why it fried..... I was left with absolutely no questions as to why this kid no longer had his own rig....