In short, yes. It's incumbent on the "user" to either know that if there are 20 items being distributed, a fair distribution can only occur at ( $n % 20 ) == 0 or to be Ok with modulo bias. And Likewise, in the case of an infinite stream, the user should either draw multiples of the size of the input lists, or be ok with the fact that as $n approaches infinity modulo bias fades into irrelevancy.
I'm also assuming that the input lists are finite in size, so the frequency can be known.
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