Why do we say "It will all come out in the wash"?

Meaning:

Things will work out/We'll find out the truth sooner or later - and there's no point worrying about it now.

Background:

This expression alludes to the power of washing to restore the appearance of clothes to their original state.

It must be said that this expression doesn't ring true in our house where, after a few washes, everything seems to have a uniform gray tinge about it.

The earliest recorded use of this sentiment is in Don Quixote by Miguel de Cervantes (1605):
'All will away in the bucking.'

To 'buck' cloth was to steep it in lye as a form of bleaching.

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