Choosing a shortest representative number from interval in arithmetic coding
While you are encoding symbols between the ranges, you are not choosing which to use for the specific symbol. You are narrowing down the possible chooses there are.  You can arbitrarily choose them per symbol, but how would you adjust the ranges to make that the actual choice. It is true that the LAST symbol you can make a choice to make it fit within the rounding error , so long as it is within the range for that symbol.

The point of the example was that the incorrect distribution gives poor or worse compression. Choosing a better statics gives better results.  Hoffman encoding is at most within 1 bit per symbol of encoding, where arithmetic coding is within a fraction of a bit per-symbol, if the correct statics are used.  You can choose how accurate you do the encoding. Increasing the length of the RANGE's precision allows for more accurate representation of the given statics, thus  less error.   Choosing the wrong distribution for the specific message, regardless of the how accurate the encoding process is will get very poor compression or make it larger than the original message.  So.. think of it is an error rate.  The smaller you can make the error rate the, closer to the real limit you can achieve.  choosing a "static" distribution for all text files, will never give you the smallest compressed file this specific method can give you.

JUST A NOTE: "Optimum" is misunderstood. It simple means that the best a specific method can be.  Not that it is the highest compression available.