I have personally discussed this subject with A DOT official. He danced around it and wouldn't admit out right that they have no authority on what a private citizens does but also wouldn't state that they definitely do have authority. It was more like well you know it's just not a good idea.
Federal agencies are generally not opposed to exceeding their regulatory authority and are vehemently opposed to doing anything or saying anything that might limit their ability to do so, or make statements that indicate that they broke the law in the past if/when they did so. A high percentage of federal government bureaucrats are in fact attorneys - and usually not good attorneys.
A couple decades ago the DOT was pretty big on going into shops and writing violations for overfills, etc, even though they have no dog in the fight unless interstate commerce is involved. There argument at the time was that scuba tanks were portable and once filled could potentially be used in interstate commerce, thus all scuba tanks fell under their purview. It took a few years for them to back off from that extreme position.
A similar example was Bob Hoover losing his medical certificate based on the observations of a couple of FAA inspectors at an air show - who apparently saw grounding Bob Hoover as a way to make a name for themselves and further their careers. The FAA required Mr. Hoover to get a psychiatric exam, and then doctor shopped to find a psychiatrist on their staff who felt he should not be granted a medical certificate, they then sent him a letter ordering him to surrender his medical certificate, which he did. Unfortunately, the FAA exceeded their authority by doing that absent proper notice and a hearing. Worse, when he asked for it back, they did an emergency revocation with no grounds to do so. After several years and great expense he got it back, and the "Hoover Bill" was passed to give pilots appeal rights to emergency actions.
It still happens in federal agencies under both democratic and republican administrations.
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Now, the reality is that I might overfill my personal scuba tanks in NC with my personal compressor and take them to FL - thus crossing state lines, but there is still no commerce involved and the DOT has no jurisdiction. Same with getting tanks overfilled in cave country and driving home with them to NC.
