In a truly-fair array of 30 random numbers 1-6, the crucial property is that you cannot predict at all how many times each number should be represented. In a single draw of 30 random numbers, if they're truly random, they might be all 1s, you don't know untill you draw. Now, if the numbers are truly random then the long-term expected average distribution should approach an equal distribution of 1,2,3,4,5,6 as you sample size approaches infinity. But it's simply not correct to say that if you draw 30 random numbers from 1-6 that you can expect to find them equally distributed---that would be a decidely non-random distribution.
Correct. But the main problem I see here is that the generation process of that 30 numbers is not described clearly.
The site may be doing it fairly, or may be not. We simply don't know about that, and so it is not provably fair.
I see (better now), thanks. I wanted to clarify that part of the OP just to make sure I wasn't completely misunderstanding.