What you say is indeed the widespread belief, and the original motivation for the distinction between /dev/random and /dev/urandom, but the truth of this belief has not been proven.
For starters, there is no guarantee that /dev/random is outputting an amount no greater than the amount of random input. (Indeed, it is impossible to prove that it did without being able to read the mind of your attacker.) For example, the patches which form the subject of this LWN story are one attempt to tweak the estimate of the randomness input because someone (Matt Mackall) thought that the current estimator was estimating something incorrectly.
My point isn't that the estimator is particularly bad -- my point is that the existence of the estimator demonstrates that there is no hard guarantee that the amount of output is no greater than the amount of input.
In theory, it is an open question whether /dev/random or /dev/urandom is more secure against cryptanalysis. In practice, they are very likely both secure, except that the blocking behavior of /dev/random introduces different vulnerabilities. (And except for a few unfortunate flaws in /dev/urandom...).
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