Service truck stuck in mud on my property: Who pays the tow?

Your rental agreement decides this, so read the site access section before you pay that bill. Every contract I've signed for jobsite units had a line saying the customer provides a firm, clear path to the unit, and that towing or ground damage from soft conditions lands on the customer. Some also say the driver decides whether the ground is safe, and if he chose to drive onto wet grass anyway, that was his call, not yours.

Two things matter in your case. First, did anyone tell you at setup that the truck would have to cross grass to reach the unit? If the unit sits on gravel and the driver picked the lawn route on his own, you have a fair argument. Second, did he call or knock before pulling onto soaked ground? Plenty of drivers I've worked with will pump from farther back or reschedule the service visit rather than risk sinking.

I'd call the office, ask them to point to the exact clause they're billing under, and ask why the driver didn't stop short. Check your damage waiver too, although the ones I've seen only covered the unit itself.

Going forward, move the unit so the whole truck access route is gravel or pavement. On my jobs we keep units within hose reach of the driveway so nobody has to leave hard ground after a rain.