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It doesn't "state" this anywhere. It's true that Subchapter S corporations, as a general statement, are not required to register with the commission, but the same is true of C corporations, LLCs, LLPs, etc...
Laws are not permissive in nature (saying what you can and cannot do), but rather are restrictive in nature (saying what you have to do or what you cannot do). The only time when you would expect to see "You don't have to do X" is when you're already in a class that has to do X by law. The laws govern who HAS to register, and then in those classes that have to register, who would be exempt. There's not a general requirement that every corporation register (in which you could expect to see a statute or regulation saying that subchapter S corporations are exempt).
So if the law doesn't say anything about corporations in general having to register, then it would similarly be silent about a subchapter S corporation having to register. It's the lack of any requirement of businesses in general or corporations in general having to register. So it doesn't "state" that S corporations do not have to register. Rather, it does not state that S corporations have to register. There is an absence of a requirement to register, rather than the presence of a non-requirement to register (yes, that is a word).
The law does state who has to register with the commission: http://asc.alabama.gov/Acts/Chapter%206_Gen_Provisions.aspx, and the website lists who is exempt from these requirements (that would otherwise be required to file under the language of the statute): http://asc.alabama.gov/file_reqs.aspx
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for the time and effort that I spent on this answer unless and until you rate it positively (3 or more stars). Thank you, ***** ***** luck to you!