Hello.
(I ain't expert on anything I state, just opinion, ok?)
Just as I need 'native speaker passport' and English tuition degree for teaching visa to bunch of Asian and Latin American countries.
If it's UK based company and person is holder of passport of country that doesn't require any special visa to travel to, it shouldn't be a problem.
Shouldn't...
Their policy is to get rid off hassle like your wife's case from what I understand.
You know, having right to live and work in the UK doesn't have much to do with 'EU passport' and exercising rights of free movement across Schengen zone. Just to remind, UK and Ireland are not part of it so that they can exercise their own border control and protection (for good reasons).
Another thing is, if she only has right to be in the UK and doesn't have permanent residency or refugee status, she isn't free to live (or work as well) in another EU/EEA country according to Treaty - one would need to check exact details of this.
Having passport that allows for visa waiver style tourist entry doesn't seem desirable to them.
Maybe, part of that requirement is that she actually works in various EU countries. Who knows. I don't know such EU labour laws.
From what I know, non-US cabin crew need C1/D visa on flights to US. That's not exactly illustrative, but shows that being airline crew one works in another countries temporarily as a part of duties. Hence I'd say it's about free movement not just visa waiver (as you experienced on your travels around Europe). C visa is temporary for airline/vessel crew and not work visa.
I dare not to guess which airline, but some bigger ones do have bases outside UK and then if one stays in Germany, France or Spain for prolonger periods ie living there, the 'papers' come into play. So some might want their staff to be flexible should such need arise.
I got EEA1 registration cert in the UK. I can get married and bring my non-EU wife from L America or Asia to UK. She could be completely legal with residence card in here, but if it's marginal or poor country, chances are she'd need Schengen visa to most of Europe and no right to work there.