One of the pennies that's been dropping for me recently is that extreme duress can provoke a mindset/belief that the capacity is not available to fulfill a particular global set of role(s), position(s), task(s), etc (in this case spanning worker/workplace-politician/father/husband/carer/human being). This "over-duress" seems to manifest as a sort of fundamental loss of core equilibrium that leaves an existential vacuum in its wake (maybe a bit like the mental spoon counter going negative), and if pushed far enough (circumstances hit the sour spot just right), I've noticed this can involuntarily be expressed to others in a somewhat irrational/illogical, clingy, needy, and unfortunately sometimes cringy way.
While I don't think this particular case is as extreme as the end-state suggested by the trajectory described above, I find it interesting that the OP of the domain has the execution to put a domain and webpage together, and has published info that describes a situation that, in theory, is still redeemable... although now that this been published I do definitely think that it's a given that there's not very much this person can do to recover their professional relationship and retain their job with everyone keeping a straight face when they theoretically next come in to work. (Cue guaranteed awkward conversation the moment they get in...)
I definitely get "just leave already, or hire a lawyer" vibes from this, but it's clear this person is at 101% emotional saturation and don't have the attention span for that, sadly. It is an excellent philosophical question as to whether this means this person's overall mental competence should be taken into question - if I'm ruthlessly honest, that's the instinctive response I have to this sort of thing, yet it's also entirely inappropriate in just about every realistic and non-realistic context I can think of. Yet it's what my brain reaches for every time. Uncanny valley is stupid sometimes.
So I guess the caveat emptor for businesses here is, sometimes people will find themselves between rocks and hard places and try to get out of them by taking you up on claims that would reasonably be immediately disregarded as fashionable puffery ("unlimited PTO" is very obviously impossible).