If you didn't agree to waive their deposits in writing or there's no agreement, I'd hold all responsible.
If one tenant (or all) caused the dryer jam, it's their responsibility. Not only did it cause mold, it very well could have caused a fire, and safety hazard.
You mentioned that the parents are cosigners. They should be aware of the documented cause. Yes it's management's word against the kids, but you have evidence of the tenants calling about the "broken dryer", AND there's related mold damage. If they insist there's more mold, so be it. The tenant (or tenants) and their guarantors are responsible for ensuring it's mold free as it was when they moved in.
Is there Tenant insurance? This DOES (or should) come under tenant liability.
We had one tenant claim that dust was mold, and efflorescence on the basement walls (the white stuff that comes through concrete, harmless) was mold damage. Sued and demanded a refund of rent (her rent was paid by the government, so trying to double dip), and showed up with a "air quality test mold report". Conveniently though, her report was "accidentally missing" the actual results and determination of the inspector, and the inspector wasn't in court either. Judge of course realized it was just to get money and dismissed her case. It didn't help her situation that she submitted a picture "of a wet basement" that showed no water, and her daughter actually confirmed that there was no water.
While it's possible in your situation that some moisture from the roof leak may have contributed a bit, the underlying cause was the heat from the blocked dryer which was due to negligence by not cleaning out the lint trap.
If it's one lease with all 4, and you have a "joint and several" clause, I'd name all 4 in a suit. If individual, then it depends on your maintenance clauses.
As Nathan said, require them to prove the existence of the mold. No doctor will say "yes I've determined it's mold... they told me repeatedly that it's because of the mold so I believe them". And of course make them prove that it's your fault. We know there was some mold, which was abated. We know what the cause was determined to be. If they prove there's mold, and can't prove the cause to be anything other than the dryer, well they've provided you everything you need for them to be responsible for a full abatement.