This company might believe that the work that they do is proprietary.  They don't want you to sniff it because they worry that you will discover valuable information that will enable you to leave them and benefit from their work.

If you sell products or services that are common and leave them, there is a good chance that they will take what they learned from you and offer similar service to another business, or set up their own business - if they are not doing it already.  This depends upon them being prevented to doing that by confidentiality language in your contract.  Otherwise it might be considered as their proprietary data.

If I was in your situation, I would examine my contract with this company and see if there is anything in there that prevents me  from visiting the account to verify that they are spending what they say they are spending and that I am the beneficiary of the entire spend.

I am not an attorney but I am pretty sure that there is nothing criminal about their arrangement with you.  But, you have no way of knowing what's happening deep down without full access to the account and all of its historical record.   You probably don't have any civil claim against them unless you can prove that they are violating a contract that both of you have signed.  This is certainly where an attorney would be helpful, if the service provider is located where enforcement is possible.  Otherwise, you will probably have to wait until your contract is up for renewal or negotiate a termination.

Based upon my own use of Adwords, I believe that things work best when bidding strategies are informed by pricing, costs of good sold, profit margins, and lifetime customer values..... and pricing strategies at the item level can't be wisely set if you only have aggregated data.  That would be my argument to get access to the account.  Bidding and selling are best done with shared data rather than things being held secret... but some people have a poor understanding of that or simply want to work behind a curtain without knowing if they are delivering best possible performance.  That's personal opinion.