Recall the literal meaning of blind spot; it's hard to believe (that part of an eye's field of vision isn't actually being seen) because it's counter to subjective perception. I claim that we mathematicians have an equally specific blind spot (in the usual metaphorical sense). When we're reading or listening, we mentally flag a logical argument as "a logical argument" that we might want to check; but we don't do the same with empirical assertions about the real world.
Let me give a demonstration, for which I first need an analogy.
Suppose you read that the most popular ice cream flavor is vanilla.
Where might such an assertion come from?
Well, two somewhat extreme possibilities are
(i) (anecdotal): vanilla is the author's and most of his friends' favorite; other writers have said so too; it's common knowledge, repeated often.
(ii) (actual data: ) someone has collected actual data relevant to this question.
One would hope, at least in an academic context, it is the latter.
Here's the demonstration. Just about every discussion of the birthday paradox asserts, explicitly or implicitly, that most people find it surprising -- indeed of whole point of an author choosing to discuss this topic is that the author thinks that readers will find the result "23" surprising. But "most people find the result surprising" is an empirical assertion about the real world. Is it true? Well, it's certainly true at the anecdotal level. Has anyone done a more serious experiment? Not that I can find quickly.
Now I don't doubt that a serious experiment would confirm the anecdotal view. But my point is that (I strongly suspect that) neither mathematician readers nor mathematician authors of such discussions ever pause to mentally flag the fact that an assertion about the real world is being made and that they might want to check whether there's actual evidence for the assertion.