Nah you totally can, they're PCP target pistols. My local sporting goods store has several. By no means cheap, and these are doubtlessly customized as much as the rules allow, but in many (most?) states they're not even considered a firearm.
They are, either (iirc) 4.5mm (for womens 25m and mixed 10m) or 5.7mm (for mens 25m rapid). I'm pretty sure he's competing in 25m rapid, which has much more restrictive rules about kit than 10m or womens 25m.
(EDIT: He was not, this was the 10m mixed team where he and his partner took silver. I had forgotten that 25m rapid uses five round .22LR target pistols and not 5-shot PCP)