A distiction without a difference.
The parks and recreation guidelines provide for private use agreements. Groups that rent for private use enter into a contractual agreement with Seattle's Parks and Recreation Commission (or whatever it's called). When someone pays a fee to use a facility it's not a huge semantic difficulty to call that a rental agreement. If you want to call it a contract for private use then fine.
Regarding the complaint that the fees charged for the Muslim group's private use of the facilities weren't sufficient to cover costs, that would also apply to every group that reserved the facility for private use. If it's a misuse of taxpayer subsidees, then the fees should be increased for everyone, or no one should be allowed to reserve the facility for private use.
Regarding the rules violations which you previously described as "many rules were broken to accomodate a religiuos group of Muslim women," I only notice: 1) your citation of the ANTI-DISCRIMINATION policy, and 2) your supposition that swimming attire rules were broken.
I think the distinction is very real.
The pool rental is subsidized. Why is the City of Seattle using tax dollars to subsidize Muslim culture which is antithetical to this countries values and to its own policy of anti-descrimination based on sex?
Why is it spending tax dollars on a religious observance?
As to their attire, I got it from the article as posted in #347. Since the article was supportive of the Muslim swim, I have no reason to doubt the reporting.
Further others on this thread have seen Muslim women swimming in full Burka gear.