Doesn't sound correct to me. The place you work at contracted with your lawn care company. Who or how your company performs the work is a total different thing.
Now if they just contracted with you and not your company total different deal. They are correct, this is to stop companys from getting around overtime laws etc.
Golden Dog Lawn Care
1997 Ford F-250/w Western Wide Out
1995 Dodge Ram 2500/w Western 7'6" Pro Plus
1986 Ford F-250/w Western 2.5 yd Tornado
Fisher Tailgate Sander
2005 Ford F-150
1997 Ford Ranger
Scag Tiger Cub