That would be fraud, but you're never going to prove it and they're going to be able to prove that the whole thing is legit. That's because it usually is legit, at least on paper. And if something is legit on paper, it's legit in court.
You seem to have your terms mixed up, though. The deductible is the part the insurer doesn't cover in a loss, which means it's usually the part that you cover. If you have $1000 in damage and a $300 deductible, the insurer pays $700 in total. If the body shop agrees to absorb the deductible, they're giving you a break and not the insurance company. The insurer doesn't care who does pay the deductible, as long as it isn't them.
And trust me, body shops don't give breaks to insurance companies. Take a damaged vehicle into any repair shop and get an estimate, then ask them how much it would be if you didn't go through insurance. 99% of the time, the price will be much lower. The only shops that give volume discounts to insurers are quick-repair places like auto glass and upholstery cleaning services.
Body shops don't give breaks to insurers for two reasons. One, the shops are doing this for money and they like getting paid. Two, everything has to be done by-the-book and with a full paper trail with insurance companies. Insurers keep detailed written records on absolutely every little thing, then make three copies of everything, because paper trails are how they cover their own butts.