I will concede that more people seem to use the word in that fashion than I thought. I will not concede that this usage:
A. is known by the majority of the English speaking world
B. doesn't create ambiguity
C. is necessary
It's funny how, when searching for comparisons of the word on the net, I came across
this page where the author seems to in one sentence acknowledge the meaning of the phrase "it strains credulity" and in the next sentence completely miss the point they just made.
Something that strains credulity would be beyond the powers of even a very gullible person to believe.
That's perfectly understandable. To put it another way, the person is generally easy to convince of things and yet this thing is so unbelievable that even they don't think it's true. The statement works by using the exceptional circumstance (that they didn't believe it when they usually do) to highlight the fact that the subject is extremely hard to believe.
This form of the saying isn't very effective because a credulous person isn't straining to believe things anyway.
If the person usually struggled to believe things then the statement would fail to make it's point. -_-
It's this sort of failure in critical thinking that corrupts language. It happened to 'I couldn't care less' and 'It beggars belief' and it seems to be happening here. I imagine the only reason 'credibility' is appearing in this particular phrase in this way is because 'credulous' has fallen somewhat out of popular usage and those who haven't heard the word before have corrupted the phrase using words they have heard in ignorance to their individual meaning. What seems happen in cases like these is the phrases become words in their own right, like how 'goodbye' came from 'god be with you'. As a point of interest, notice how after the constituent words lose their meaning the whole phrase can change meaning (Do you wish god to be with people when you say it, or has it just become a thing you say when parting?).
I find it interesting how people corrupt language but I don't think it's pretty. Poor critical thinking annoys me and poor use of language is a symptom of it.
EDIT: I'll also note how I'm enjoying this topic a whole lot more than the one about whether the game is dead or not. I'm pretty sure we've had that discussion more than a few times already and I still fail to see how something can be dead when there's still life in it.