Obviously, I say bury the pipe. As to its depth, 18" is fine. Just get it WRITTEN into the contract. Make sure you talk to him about a gravel/stone bed. If the pipe is perforated (which I'm assuming it's not), no gravel is necessary. BUT, if it's perforated, 4" of gravel on the bottom, 6" on top, and WRAPPED in filter fabric (or landscape fabric, preferable the ff.)
You can always cut up a few Pressure-Treated 2x10's into 3' lengths, or so, and lay them perpendicular across the area in question, and drive over them. The only downside is if the ground is really soft, they'll leave 'depressions' in the lawn. You can rake the area with a thatch rake and have the grass grow back after you remove the planks but you'll still have the depression. Use PT lumber because it won't rot.
Another suggestion is to have him use residential-grade sewer pipe for, say, a 20' streatch of the pipe's run. That way you won't crush it for sure at 18", and, you won't have to use planks. Just, somehow, mark your lawn where the metal pipe begins and ends.
One last suggestion, if the heavy equipment is only a temporary thing, don't bury the pipe until there's no more heavy equipment being used. Then bury it 18". I'm not so concerned about the truck as I am the forklift. If you need more info/guidance, e-mail me directly. (This post is getting burried quick on the forum!) My best to ya and hope this helps.