A few weeks ago, it was stated on the podcast that if the universe is infinite, you get the situation where eventually you will have other worlds that have a Pamela and Fraser on them.

I do not think that this is necessary (or likely for that matter). Even given an infinite universe, repetition is not required. Take the number line, you can have an infinite series of even numbers.. To achieve an infinite amount, you DONT have to include odd numbers or allow repetition.

Of course, a number system is by definition non-repeating. In the universe, its definitely the case that the situation CAN arise again, meaning the
probability is not 0. In fact, isn't it the case that the probability of an identical world is non-zero even if the universe is finite?
By believing in repetition, we are assuming a finite number of possible chain of events could occur, leading to a required repetition (deeper philosophical question, if all
things are exactly the same (even quantum state) are they in fact different
planets or the same planet?).

I guess the question comes down to the question are their a finite number of
possible arrangements of matter in a universe which requires the assumption
that the infinite Universe is uniform (same laws as we see them apply
everywhere rather than variations over certain ranges, which I think is
reasonable considering we have yet to see anything to the contrary).