That is absolutely a fact. I got a flat a couple of weeks ago and didn't have the wheel lock thingy with me in the car (stupid, I know!).
First tow truck company wanted me to sign a release agreeing that they were not responsible for damage. Second company I tried was much better. They used some wooden boards to get the car onto the flatbed. Even then, I got some damage to the front.
Don't forget, if you have a flat tire, the car will sit EVEN LOWER.
(BTW, I have a V2 front bumper and the car is lowered on Nismo suspension)