We are a privately held company and it is not uncommon for large OEM customers to request financial statements on our company as a critical supplier. While I understand their concern, it is against our policy and ultimately the owner will not allow the release. I am looking for suggestions on how to satisfy our customers concern for viability while also abiding by the owner's wishes and keep the customer.

How to handle customer request for the supplier's financial statements.
Answers
Instead of providing the actual financials have a "analyst call".
Discuss the large picture, the ratios, the business (plan, forecasts, etc). It may just suffice.
Unless you have monopoly of the product/service or your product/service is waaaaay ahead in quality from others, your owner will have to budge/change his mind or forego the customer. It also depends on how important or critical this customer is to you.
I do NOT understand the "against our policy" part. If the financials play an important role in acquiring or maintaining a customer, or for that matter obtaining a loan (for instance), why have that kind of policy?
You have to understand that companies (especially public ones) are under constant pressure to KNOW THEIR SUPPLIERS. From a delivery dependability standpoint to a SOCIAL RESPONSIBILITY standpoint. I have seen public companies ask for information on suppliers further down the supply chain.
You don't say who at the large OEM company wants to see the financials. Is it the head of Strategic Sourcing or a junior purchasing agent?
I would offer to have a meeting with the former; I would tell the latter they can't have the info, but their VP is welcome to have a call with the owner.
If you are a company that gets an annual audit/review done, you could perhaps just share the
I like Pragya's idea. If that doesn't suffice, perhaps the auditor's opinion along with your bank's opinion would be enough, especially if you have a loan or credit line with them.