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Replace & Rationalize

Further to a question on Stack Overflow I noticed a puzzling
evaluation.  Why does the second expression generate reals?

(x \[Function] 
   If[IntegerQ[Rationalize[x]], Rationalize[x], x]) /@ {0., 1.}

{0., 1.} /. x_ /; IntegerQ[Rationalize[x]] -> Rationalize[x]

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