Wildcat66,
Here is how it works:
1. Clubs/Leagues rent the fields from cities or private parties. The fields during those rental times are subject to the rules and regulations of Cal South, the respective Clubs/Leagues, and the City/Private party.
a. In the case of a public park, the areas outside those areas rented and controlled by the Club/League remain subject to the rules of the park, but inside the area rented, guests (including "dog walkers") are subject to all the rules as noted above and may be removed by representatives of Cal South, the League (CSL, SCDSL, Presidio, etc.), the Club (Coach, Manager, etc.) or the Agent appointed by Cal South, the League or the Club also known as the Referee.
b. Most contracts/rental agreements provide that the "entire grass" area is rented, which means that the folks holding little Jenny's 4th birthday party near the playground are violating the Club/League's space when they set up their jumper on the corner of the grass field 70 feet from the soccer field.
2. Folks in the vicinity of the fields (or on the areas rented) are subject to the rules regardless of whether they signed a form or not because for that time being, they are guests on property controlled by another (in legal speak they are "Licensees").
3. With respect to dogs, most leagues have a "no dogs" allowed policy. So, if you are in a public park walking your dog, I recommend you watch the games from a distance because once you bring the dog within the areas rented/leased by the Club/League you are now subject to their rules and they can politely ask you to remove your dog from the area, stop being abusive, etc..