Well if there isn't the evidence, it's difficult to rely on it...You have to find other sources for reference or simply say 'I don't know'...
But...
Most of your augment for the existence of these chaps is the sort of negative-proof... The lack of evidence against isn't evidence for...
The whole of my point is that we have one source for this type of cavalryman... they don't even appear anywhere else in Derrick... Mostly his images are historical... But... very late in the piece, which is plate, 10 or 12 of 15(?), at the very climax of the tale he's portraying... the final rout of the Irish... in my opinion... (the lady with the knowledge was reticent about drawing conclusions).... he makes these up... a kind of crusader knight riding down barbarians, with allusions to Arthur, that the readers of the time wouldn't have missed... The lances and big crosses are a clue... the educated 16thC mind was very good at connections between allegory and actual events... and the art is littered with anachronistic clothing, building and armour/weapons types which are supposed to convey meaning to a viewer...
It's not a popular view...
Not unlike trying to tell all those folks that game 'Arthurian', that most of what they think they know about the 450's - 600's is doubtful at best... People like their histories to be a little fantastical...
Derrick did that for his viewers in the 1590's... These minis do it nicely too...
But historically accurate? no, not for me...

(I was horribly pleased to have smartly sidestepped the whole issue when I came to looking at Tudors minis to make... we weren't making the minis for 1590, so I didn't have to disappoint people who were expecting them...)