What people said before are right.
You can substitute different dice rolling techniques as long as they have the same probability distribution.
Rolling a d4 is equivalent to rolling 1-25 on d% because the probability distribution is the same (again, assuming it is fair).
Your argument that d4 and rolling 1-25 on d% are different is valid only if one or more dice are not fair (have an equal probability of landing on any of its sides). If that is true, then yes, the probabilities will be slightly different, but in a way that it difficult to measure. If any die is not fair, the all of this goes out the window and you really cannot compute actual probabilities or say which is better unless you have mathematical data that describes exactly how much more likely one side will come up with another, and that just isn't practical in this situation.
In fact, no die is perfectly fair. The grooves where the numbers are on each side are certainly not the same size (or if the numbers are painted on, the amount of paint for each will not be the same. The 20 side should weigh less than the 1 side on dice with carved numbers since more material is carved out of it. But the difference is so small that it is not noticeable and can be disregarded from the probability calculations.
On a very fine level, your analysis that two dice could make a very slight difference as opposed to one is correct, but the difference in probability is also negligible. Basically, you are making this factor much more important than it really is.
The moral of the story is that a d4 is just as good as a d% in practical use, as long as the player is rolling each properly (for example, tossing the d4 and giving it a noticeable twist instead of just letting the d4 slide out of your hand and fall on the table). If you are seeing a big problem with the d4 giving extremely skewed results even after many rolls, then test it yourself, correct the player's rolling method, or ask them to use a new die.
Th DMs word is always final, but if you are trying to argue that there is a significant difference in probability of rolling d4 versus 1-25 on d%, then you are incorrect because there is not (the differences are negligible unless the die is really grossly unfair, in which case, you shouldn't be using them anyway).
Jason.
(Not a Statistics/Probability major, but had 12 credits in Statistics/Probabiliy in college at Penn State.)
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Actually, if it were possible that you could hold the same die the same way every time and applied force to the die exactly the same way every time you threw it, you should get exactly the same result on the die every time. It is because humans cannot do this that a die is "random" in the first place.
