Multiple Health Insurance Policies

Hi. I was wondering--if you are covered by more then one health insurance policy, is it ever possible that you would get less reimbursement then if you were covered by just a single individual policy?

Here's my situation: My wife's current insurance allows in-network specialist visits, which she uses frequently, without a referral with a small ($20) co-pay. I may be able to also get her covered by my insurance for basically free, which would then be secondary to her current insurance. My insurance covers everything completely, but has a very annoying, arduous referral process which she would probably skip since she has to go to this specialist frequently.

What I am wondering is this--without the referral my insurance (which would be her secondary) would likely not pay anything for the specialist appt. Would her current primary insurance (which currently covers everything except a $20 co-pay) be able to say that they won't cover the specialist appt. fully because her secondary insurance should have paid some, and that she should have gotten a referral from the secondary insurance before the appt?

Thanks a ton!