Yes, they can, if they are impeding the use of a public right of way. When someone parks a car on the (public) street outside of your driveway, blocking you in, you can call a tow company to have it removed, and they would be legally justified in removing it and charging the owner for the impound.
It's kinda established that if you park like an asshole, someone might call a towing company, and they'll charge you a fee to release your car. In that case you've got a potentially shady towing company and their legal people lined up against an individual who owns a vehicle that was parked somewhere problematic enough that the tow company was prepared to risk towing it.
There's a different power dynamic when it's small local shady towing company versus VC backed "growth hacking" disruptive startup, who potentially have some fairly high powered legal services if not on retainer themselves, quite like available to them via their investors or stop accelerator...
I read recently Uber were talking about getting into the bike/scooter rental space? Pretty sure I'd advise against local small business towing company/franchise from risking getting into a lawyer fight with Uber...