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If Bishop Adamson is a legit RC bishop willing to ordain resistance priests, then why did OLMC resort to Ambrose?  Is he a sede? Surely when Fr P was beating the bushes for a more co-operative bishop he didn't pass over a RC for an Orthodox? Somethings fishy...

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Who said I had a hard time finding them?  It's remarkably easy, because with the more respectable of the traditionalist clergy, this information is quite easy to procure.
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Nor will I "become" his flock.  Because a) the very fact that he thought Pfeifferville was a good place to be formed as a Catholic priest is a major indictment on his judgment, b) Catholics do not, contrary to common believe "choose" pastors, but have pastors sent from the Church-- what we do is prudentially decide, from one priest to the next, whether to avail ourselves of sacraments he can confect, despite his status as a complete non-pastor (a pastor is someone with jurisdiction to whom has been given the care of a certain flock by the authority of the ordinary), and c) I would never patronize a man who couldn't prove his orders, since even if everything else checks out, if he can't make real sacraments then he's not of much use as a priest, is he?
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The request is not for docuмentation of their entire lineage, the request is for docuмentation for whatever part of their lineage that occurs outside the supervision and explicit approval of the Church.  
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Nor are any of these priests or bishops legitimate.  That's the whole point, Fanny.  None of them "come from the Church."  They've all, down to the last man, procured their training, sacraments of orders, and exercise their ministry outside of the Church's framework established for doing so.  If they didn't, there'd be no need to ask!  But they have, and that's that, but as a consequence, we do not have this blanket presumption of validity that can be extended to every Tom, Dick, and Harry who says "don't worry, I have Thuc lineage."  
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Even if these men were fully legitimate, the onus is still on them to prove it, even in ordinary times. That's why the celebret is such a big deal.  Priests would carry it with them always.
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If this is uncomfortable for certain priests, I don't know what to say except "too bad."  The belief that a man who claims to be a priest has a right for people to believe him without proof is anarchic and tyrannical.  Faithful are within their rights, indeed they are duty-bound to know whether the man they are patronizing is really a priest-- asking for such proofs is not trouble-making, but playing fast and loose in providing them is.
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For my part, it doesn't look like it ever occurred to Francis that he should make sure that Adamson was a bishop (that is, beyond just looking it up on the Internet to see if people called him bishop).  It's nice that he had the decency to docuмent his own ceremony.  Good for him.  But that's just one piece of the pie.  If he can show that Adamson is a bishop (which requires showing that everyone who "led up" to him was a bishop), then he checks out, and at least the single most important condition is met: the man's a valid priest.  Still lots of considerations after that (does he believe rightly, is he of sound judgment, and whatever other conditions a person finds prudent to have met when deciding whether or not to avail himself of the priest's services).  But at least the most important condition is met, and people at least know of one other priest they can call on their deathbed.