If we were talking about coverage provided by your insurance company, then the issue would be fairly simple - it would depend on the terms of the contract you entered into with them (your policy).
However, since we are talking about a situation involving an entity that you do not have a contract with (i.e. someone who is insuring someone who has done you harm), the situation is a little more complicated. Technically, you have a claim against that other person, based on which you could sue them and ask that a court order them to pay you damages. What damages a court would deem appropriate might differ from situation to situation. It could be an amount consistent with the use of OEM parts, or it could be a different amount.
In this case, the insurance company's obligation is to their client, and they don't have any specific contractual agreements with you. However, in order to fulfill their obligation to their client, and depending on the specifics of that obligation, they will usually seek to reach an agreement with you as to damages, and in so doing remove any potential civil claim you might have against their client. If you can agree, then all is well, and the situation goes away. But, if you are unwilling to accept what they are willing to offer, then you have the remedy of suing for an amount that you think is appropriate to make you whole. Fundamentally, it is a negotiation. Your leverage is the threat of a civil suit and a potential complaint to the Maryland Insurance Administration, and their leverage is that you want the money and don't want to go through any more hassle than you have to.
So, there isn't really any easy answer. If you don't like the offer they make, and don't feel like it is fair - then ask for whatever you think is fair. If they refuse, then you have to decide whether or not it is worth the trouble, expense and risk to take it to the next level.
Depending on the situation, it is also possible that your insurance company will handle the situation pursuant to the terms of your policy, and through subrogation seek reimbursement from the other insurance company.
And just to be clear, I am not a lawyer.