Primary health insurance interfering with secondary health insurance

Short answer is "no, this situation (secondary denying coverage because primary denied) is uncommon". Typically, your secondary coverage will cover up to its limits any parts left unpaid due to lower primary limits.

I talked to a US health insurance expert who has worked in the industry for decades. Here's what he said:

• If you go to the hospital, you are covered by your health plan. So this situation wouldn't occur in an emergency situation
• If you have some experimental treatment or something not covered by primary, it also wouldn't be covered by secondary, but even if you only had the secondary provider they wouldn't have covered it anyway.
• In the situation where your primary doctor ordered a treatment which they thought was medically necessary, and your primary insurance denied coverage because they determined it was not medically necessary, you need to go through the standard appeals process. If all steps of the process fail and it is finally determined that the treatment was not medically necessary, then yes, he said that secondary insurance would almost certainly use that as a reason to also deny coverage.

But in standard, medically necessary treatment, he says the hypothetical situation you described would not be very likely to occur because medically necessary treatment will be covered. It's just a matter of co-pays and deductibles and secondary insurance making up the balances.

He also said it's common for people with two insurance options like this to turn down their employer's insurance and just sign up with a spouse's policy. Pat isn't necessarily "worse off", in terms of total out of pocket expenses, but will have more paperwork submitting claims to secondary for amounts left unpaid by primary's coverage limits. In that sense, it might make sense to only get the spouse's better coverage.

is Pat worse off by having what one would reasonably believe is "more" health insurance?

Yes.

Especially if the partner's insurance has significantly better coverage. Some companies will even pay you a cash benefit for not using their health insurance but going with partner coverage.

are these all fairly "normal" things that could happen

Best practice is to avoid this scenario. Just pick the "better" insurance for both partners and stick with a single one. Hence it's only "normal" for people who choose two insurances which isn't all that common.

The main issue here is that insurances will go out of their way to deny claims and the presence of a second insurance will make this easier for them since they can always blame or leverage "the other insurance".

Pat's primary insurance denied the claim, the secondary insurance (through Sam) also denies the claim.

Every insurance has their own terms and conditions which are lengthy, complicated and full of coverage exemptions mechanisms. For every specific case you would have to read to the applicable terms and conditions. It's entirely possible that the secondary has exclusion claim that says "If the primary denies a claim, we also deny the same claim".

Whether that would hold up to a legal challenge is anyone's guess, but insurances are perfectly fine with aggressively denying claims and fighting in court if needed. Court cases cost a lot of time and money and many patients don't have the stomach or resources for it.

... the US healthcare system sucks in a big way.

It sure does. It's eye wateringly expensive (most expensive in the world), and the health outcomes are mediocre at best. A good example of how immoral this companies behave are "Pharmacy Gag clauses", where they excplicitly forbid a pharmacist from telling you when it's cheaper for you to pay out of pocket instead of using the insurance (with co-pay). See https://pmc.ncbi.nlm.nih.gov/articles/PMC6293384/