I think there is still a roster limit, regardless of your mix of scholarships/walk-ons.
It was a Joke.
I donāt believe you can move down once you have a scholarship? I could be wrong on this though. In football, I believe there is a rule that you canāt be recruited as a walk-on if you take an official visit to that school. Not sure if thatās the case in basketball as well.
It must have been because I donāt think there are 17 students in their entire university with academic scholarships! Joking! 
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But that is the factual part. 
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If you are a walk-on, the scholarship can be awarded to you for the rest of your career or on a year to year basis. For example, if a junior walk-on was awarded a scholarship because there were only 12 scholarships on the roster, it does not mean they automatically get the scholarship the following year. They could, strictly based off what the language says in the scholarship papers.
An example, my wife is a D1 track and field coach. They write their scholarships based off of four years and will guarantee that specific money or percentage for the four years. If the athlete performs better or another scholarship athlete leaves, the athlete can be awarded more money on a year to year basis or for the rest of their career. It can be really tricky with the math because they only get 18 scholarships for roughly 70 women. Not all athletes are on scholarships but the range goes from $1,000 to a full ride.
Yes, itās different than the 13 full scholarships that basketball gets but I hope I made it clearer.
In football (or any sport for that matter), you can go on an official visit as a walk-on. There is (or was) some different lingo that categorizes walk-ons into two separate groups but itās too much to explain.
Forget this post.
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Yes, and there are a couple of exceptions I know of. If you award a scholarship to a freshman walk-on, itās a four year guarantee in the Big Ten. Thatās to keep schools from getting around class size limits, particularly in football. Football also has a category called blueshirts, which applies only to recruits if they donāt take an official visit and donāt receive an official offer. Theyāre not walk-ons. They get a scholarship as freshmen, but count as part of the following years recruiting class. Iām pretty sure that is only for football, but itās easy to mix up the various rules.