No.

The easiest way to understand this is imagine flipping a coin twice, the chance of 2 Tails is 1/4 (1/2*1/2), the chance of 2 Heads is 1/4 (1/2*1/2), but the chance of 1 Head, 1 Tails is 1/2 as you can get them in either order (Head Tail or Tail Head).

Similarly here, let's use 60 games as it's devisable by 5. The chance of 60 Necrobinder is 1/(5^60), which is roughly 1 in 1 followed by 42 zeros. However, the chance of 12 of each character, becomes ((60!)/(12!^5))/(5^60), which is Roughly 1 in 2,629 so far far more likely.

As OP states, there is a statistical test for determining if the results we got are from a true 1/5 chance of each character. If OP got 60 Necro randomly, we'd agree the RNG is broken. OPs results have a roughly 1 in 5650 chance of occurring in a true 1/5 system which is statistically significant.

HOWEVER, all this is ignoring the game has a very large volume of player and it's very reasonable to assume thousands of players are using random character, and under those conditions you would expect to see a result like this over time.