It all varies by state, and if the DOT number you use is an intrastate or an interstate number. Once you go interstate, then you have to abide by all the federal laws and inspections (safety, fuel tax, etc.), but the only way I see an LCO using an interstate DOT number is if they operate in multiple states.
I have an intrastate DOT number, as most people should, so I have to abide by my state DOT regulations, not the federal regs. So, in MI, CDL is required when your GVWR is 26,001+, 16+ passengers, or hazmat.
The Chauffeurs License is the second option here. If your GVWR is 10,001 and used commercially, you need a Chauffeurs, also applies to driving passenger vehicles like taxis, limos, etc.
Like everyone says, it just applies to your state. If you're never going to run anything more than a one ton, then a CDL isn't really required. The problem is, you hook your F350 dump truck up with a GVWR of 19500 to an equipment trailer with a GVWR or 10000, you're in CDL territory.
I have a Chauffeurs myself.