Am I the first to laugh at Eliezer's scenario?

It's very simple: Mary was much more likely to be a liar than a virgin mother. This is true even if you assume that there are virgin mothers who are their own granny.

And the point is even simpler: don't ignore the outlandishness of a claim just because everyone believes it.

(But I would also not advise you to judge a claim according to an unbeliever's caricature. Make sure it's not a strawman.)