Delays, especially speech delays are a known cause of behavioral problems. They get frustrated so they act out.
STs also work with social skills and can teach appropriate behavior and coping mechanisms that could be beneficial to all kids.
In my area, they can't do anything without consent, which can be revoked at any time by the parent. After you leave the program, the records get sealed (at least it used to be). It doesn't necessarily mean there's going to be a label that follows them forever. Minor delays aren't uncommon and sometimes kids just need some short term assistance. It's much easier to take care of these problems sooner than later.
And even with an independent eval, they still need to do one with their people. What a private dr. says and what a school can afford to treat aren't always the same.
And IME, the therapists themselves that will be doing all the work have a big say on who gets what. They have limited time and resources and can't afford to waste it on kids who don't need it.