However, a married person who is polyamorous is either a serial liar or in an open marriage. It’s reasonable to infer the latter since it is the least offensive.

Polyamorous people can still marry or be married. That doesn't somehow make them "serial liars" or otherwise result in them being required to describe their relationships using a specific term such as open marriage.

This depends on your definition of "open marriage", but to be clear, polyamory is _not_ about open relationships (which I think "open marriage" suggests). Polyamory typically means closed/committed relationships, but with multiple people. That they are made out to be sleeping around or in less serious relationships is incorrect, at least as far as the terminology goes. I would not say that a married poly person is necessarily a liar or in an open marriage.

You seem to be unreasonably narrowing options here for no reason. A polyamorous couple could date others, as a couple, without it being an open marriage

My understanding is that an open marriage bars long term amorous relationships from the mix, but that things are ok