As much as I hate to burst your bubble, this is in fact a D.O.T. recordable accident. You did not have to get drug tested becuase you were not cited. You can check the company out on Safersys.org in a few weeks to see if the accident is listed. If it is listed on the website it will also be on your PSP report for the next five years. Most companies will hire with only one major accident but i do not believe I would tell them about crossing the highway and three ditches before hearing a pop. Try and get a copy of the accident report to see what it has listed on it. It might be helpfull on future interviews, especially since you were not cited.

Question , you said you reported a steering problem and they said run with it or it's not a problem .. Did you by chance write that up on a DVIR and have them sign that it was not a DOT issue to keep the truck from safe operation ? If you did you will have a leg to stand on . Second thing you might have done is ... Did you Qualcomm it into dispatch and they respond with something like RUN IT , or IT'S NOT A ISSUE ... Etc maybe you have a email transaction anything . The above mentioned will help your case .. Maybe not solve it but help

By reporting it via phone or just talking to a shop guy will be hear say unless of course you recorded the conversation .

Any towed vehicle is a DOT reportable event