The coach talking about your son being a walk on candidate is basically telling you he doesn’t have the ability to offer any financial support. Some schools do not have the money available to fund the NCAA scholarship number. A fully funded program CAN pay for up to 9.9 scholarships but a partially funded program may only be able to fund 1 or 2 and they divide the number up among upperclassmen. Every team will operate differently and just because they are allowed to offer a certain amount, doesn’t mean they have it to offer in the first place. Perhaps there is an option to get financial support with the more competitive times requested but again, that can vary by team and how the coach decides to manage his resources.
I know a family with 2 swimmers, one is going to be a first year at one of the schools you mentioned and the other will be a junior at a different school you mentioned. One gets nothing for swimming (power score of 45) and the other is gets a very tiny amount, well under $5K, with a power score of 39. Sadly, the money just isn’t there for the vast majority of programs.