Towing unattended car from I-10 – legal??

Today I had a flat tire while driving on I10 towards Katy, and deemed the situation too unsafe to try to change the tire while on the shoulder (tire was on the side of traffic).

I called State Farm for a towing truck, they told me I could leave the vehicle unattended. Since the arrival time was about 1 hour, and I was too nervous about the speed of cars going past me (have seen too many Final Destination movies), I decided to leave the car there. 30mins later I get a call from the towing service telling me the "city" towed it before he got there. However, it was towed to a private location and the Houston police have no record of it in their system (findmytowedcar.com)

1) Is it illegal to leave the car unattended while waiting for towing? (Considering the unsafe situation)

2) Is it legal for some random towing company, apparently not associated to the City of Houston, to just tow my car from the highway??

I can't even pick it up today because they are closed, have to wait until Monday. Also, the initial towing service (the one managed via state farm) gave me a number to call and said "don't say I gave you this number".. andd how did he even know where it was taken?