I have this table from my "benefit maximums" page of my American health insurance:
There appears to be both a benefit maximum (second row of first table) and an out of pocket maximum (first row of second table).
If both maximums are hit than the rules say I won't have to pay because of the out-of-pocket max but also that they won't pay because of the benefit max. So which rule wins?
Note that in the first table, the items apply to annual out of pocket maxima. This is because what is being shown there are your deductibles. The maximum deductible you could face would be $6,300 if you only used in-network providers, $12,600 if you only used out-of-network providers - and $18,900 (the sum of the two) if you used a mix of in- and out-of-network providers.
Table 1 is telling you that you may experience higher deductibles than you think you will, because they track in- and out- providers separately for purposes of deductible accounting. The 'maximum' (unhelpfully provided under both columns) represents the worst case scenario where you max out both deductibles.
Note that in the 2nd table there's the same relationship between the first value in each column and the 2nd value given in both columns - the 2nd value is the sum of both first values.
Table 2 is telling you that, if you only use in-network providers, your maximum out-of-pocket is $9,100. If you only use out-of-network providers, your maximum out-of-pocket is $20,000. But if you use a blend of in- and out- providers, because they're tracked separately, you could end up $29,100 out of pocket in a single year.
Suppose you incurred $7,000 in medical expenses from a single injury, and were seen only by in-network providers. Assuming you're 0% covered before the deductible is maxed, and 80% covered past the deductible, your out-of-pocket costs will be in the vicinity of $6,440 - you are paying up to the deductible, at which point the coverage kicks in for the last $700, of which you are responsible for 20% ($140).
Your deductible for in-network providers is now maxed out ($6,300), and your out-of-pocket maximum is 70% used up ($6440/$9100). If you get hurt again, and incur another $7,000 in medical expenses AND:
You get badly hurt and incur $10,000 in medical expenses, you go see an in-network provider. Still assuming 0% coverage, then 80% coverage after deductible.
Your bill is $7,040 ($6,300 deductible + 20% of the remaining $3,700).
You then get hurt even worse and incur $50,000 in medical expenses and you:
Go see an in-network provider again. Your cost is $2,060. Your coverage, post deductible, means you're still responsible for $10,000 but after that $2,060 you've reached your out-of-pocket maximum for in-network providers and your insurance is now covering 100% of the remainder. You will not have to pay anything for any medical care for the rest of the year as long as it's in-network.
Go see an out-of-network provider. Your cost is $20,000. First you have to pay 100% of medical expenses up to the deductible for out-of-network ($12,600) - then you owe 20% of the remaining $37,400 ($7,480) - bringing your total to $20,080 - but your $20,000 out-of-network out-of-pocket maximum kicks in and they most graciously swoop in to cover 100% of that last $80 for you.
TL;DR - These rules don't conflict, they're just bad at making useful tables for you. The first table is about your deductibles, and how you can end up paying more than you think if you mix-and-match in- and out- of network providers, resulting in a true maximum deductible of $18,900. The rules for what's covered and by how much changes at the deductible. The second table lays out the out-of-pocket maximums and that represents your true maximum liability for anything. Your insurance is covering 100% of anything beyond that point.
