Actually, it would be very easy to make the probabilities exactly as stated, and it wouldn't depend on the statistics of the process. They could:

a) simply use a deterministic process that simply walked through the letters at each position and assigned them.

b) Used a "random" letter picker for each position (knowing that it is not trule random), but throw out each letter than is chosed. This way, the distribution would, again, be exact, and more "random seeming".

Easy to do...even for AA.

Cheers.