Sampling from a probability distribution is equivalent to lossless decompression

This idea as described in the article only works for specific distributions, because Huffman coding is a prefix code, and is only optimal for distributions with specific characteristics. Think of a two symbol alphabet with P(A)=0.1 and P(B)=0.9. Huffman coding is very poor on this, and your decoding or a random stream definitely does not have the desired characteristics.

If you want to make it better you need to step to something like Shannon-Fano coding which works on collections of symbols and approximates the distribution much more closely.

On the other hand, you can step sideways to Arithmetic Coding and get exactly the distribution you want in a single clean and elegant model.