Of course, their view is backwards. It's inverted. The doubt already exists due to the changes in the rite. There's nothing more to prove.
No, this is the hill I mentioned. Although we ourselves do not know, somebody knows when it is valid and when it is not. Both the sedes and the SSPX claim they have the knowledge to know - one knows it's valid and one knows it is invalid. Either both are idiots or only one of them are idiots because they cannot both be right. Which is it you tell me?
Per the earlier link, the SSPX deem the rite is valid when done by the book. This is because they claim the Rite, when done by the book, is
"not subject to positive doubt" - why do they say that? Because they claim that the matter and form is
"practically identical to those defined by Pope Pius XII" along with some other reasons in the link. You disagree, I disagree, many (most?) trads disagree.
You say because they changed the established rite that there is positive doubt, I say the same thing along with tons of other trads - but the SSPX does not and has never taken that position. They accept the rite as valid yet investigate the same as they have always done ever since new rite priests started coming over to them.
Yet, they consecrate their own bishops.