Absolutely.
Chance that a legendary is primal = (1/400) = 0.0025
Chance that a legendary is not primal = (399/400) = 0.9975
Chance that none of X legendaries are primal = (399/400)^X
Chance that none of 2000 legendaries are primal = (399/400)^2000 = 0.006695896276
i.e. roughly 1 in 149 players would get that result, which is a completely believable claim.
But the claim was…
The chance of not getting any ancients in 1970 legendaries came out at 3.3 in 10^92. There are 10^80 atoms in the universe. The chance of this streak happening would be the equivalent of picking one specific atom out of one trillion universes this size.