Without knowing how the generated numbers are being used, I can't comment more specifically. Different seeds would most definitely yield distinct streams of pseudo-random numbers.
However, the practical random number stream is influenced by how many possibilities they are testing for with each call to the random number and how many number of times the function is called. For example, if you are using a random number to check for a pass-fail--even if you weight the results due to player characteristics/strategy, etc--it still comes down to a test of even vs. odd numbers. So for each call, there would be between perhaps 30 to 70% of all random numbers that would allow the same result.
Now, the chances of this happening exactly the same way twice with different random number streams obviously decreases with each successive call (and even further if there are more complicated decisions happening), but it's not like an incredible lack of randomness gets noticed on a weekly basis.
People should be happy, given an assertion from admins that there are at least some random factors, that by and large if you build a strong team and make strong tactical choices you are going to get rewarded for it.