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