I'm not sure it was a flimsy pretext, as it depends on whether there was a valid prior engagement to Eleanor Butler. That's one for people more expert than me to decide. ITTL it will be politic for people to accept it as valid though. And I agree Richard won't raise a bastard to be his heir, instead he'll look for another bride. Or, nominate a surviving nephew or more remote connection. Who would be accepted as heir if Richard died before marrying anyway?
Regarding how the nobility regards Richard after his quick action to kill off the Stanleys - I would reckon stunned at first, worry thereafter. Which might translate into forced retirement as his earlier namesake at some point. Possibly in favour of a son or a.n.o.. I doubt nobles are happy with such arbitrary (as they'll see it) execution of their peers. The Scots got rid of James III in the 1480s so there's another example.
BTW, what's the blog consensus on the deaths of the Princes in the Tower - Richard or Henry Tudor? I've always been partial to the thesis of Truth is the Daughter of Time but I'm aware it's not the academic consensus. It does strike me as unlikely that Richard wouldn't have publicised their "sad deaths from fever/whatever" had he been responsible but maybe he had a reason.
It would not have been flimsy if somebody had brought it up as soon as Elizabeth of York was born, or even as soon as Edward IV married Elizabeth Woodville. But bringing it up a decade after the marriage was fait accompli, and with Edward IV's children having been accepted as legitimate since birth, was kind of flimsy. Richard would have to be very correct about his own children's status to avoid similar events being possible.
In OTL many people seemed to believe that John de la Pole, Richard's nephew by his sister Elizabeth, was heir to the throne. England had already confirmed that succession could pass through women, with Matilda and then also with Edward IV's claim descending more closely from a granddaughter of Edward III than any grandson. So, since all of Edward IV's children were named bastards, and Edward IV and Richard's brother George's children attainted for their father's treason, the next in line is Richard's sister Elizabeth of York, Duchess of Suffolk. Though apparently many seemed to think that it would simply transmit through her to her son John.
The precedent for Richard killing that Stanleys is indeed negative, but he has no tangible domestic enemies at this point. The mightiest men now existing in the realm all fought with him at Bosworth, and are infuriated that the Stanelys would sit at the sidelines and making sure to opportunistically join the winning side. The precedent of confiscating the lands of relatives of condemned men is hundreds of years old at this point.