No, they don't. That's the point of liquidated damages clauses - the amount of damages in the event of a breach must be hard to prove, hard to figure out. If you could easily put a dollar amount on it, then liquidated damages are not appropriate - you would just measure the actual harm caused.
I don't think the doctrine of liquidated damages is the right lens through which to view this. For the non-lawyers on the board, when someone breaches a contract, the plaintiff ordinarily has to prove how much it was damaged by your breach. To use an easy example, if we have a contract for me to sell you my house for $100,000 and you don't come through, and then I try to sell it to someone else and the best I can get is $80,000, my damages are $20,000 (plus any additional costs from trying to make a second sale, etc.).
Liquidated damages is a concept whereby you don't have to prove your actual losses when someone breaches your contreact. Instead, the contract has a clause that says, basically, "if you breach your obligations, you will pay me ___ in damages." These types of clauses are usually enforced only if it would be difficult to prove the amount of actual damages. So, ordinarily, you couldn't get liquidated damages in the home-sale example I used above, because actual damages are reasonably calculable. The law disfavoring liquidated damages clauses makes sense because liquidated damages provisions are usually drafted by the contracting party with more bargaining power, so the law protects the weaker party.
Here, while acknowledging that I haven't seen the exit fee clause in the ACC bylaws, I don't see this as a liquidated damages issue. I don't believe Maryland breached the ACC bylaws by withdrawing. It did what it was contractually entitled to do, but that contractual entitlement comes with a set cost. That's not liquidated damages for a breach, but an agreement that schools can withdraw but have to pay a set amount to do so. Looking at it that way, where there's not a breach but a set cost for defined conduct, I think the only defense is unconscionability, which is NOT a favored defense in the law and one that is almost never available to a sophisticated party. That's how I'd pitch this if I were the ACC and I think I'd be right about this.