There's a guy in another F150 forum having the same problem. Only suggestion there so far was to use a Dremmel type too to cut off the offending bolts from the backside of the grille. Thought there is that he will eventually need a new grille surround anyway - and of course you can't buy just the surround, you have to buy a complete grille from the dealer.
Your truck accessory dealer may be talking about snapping the grille surround off of the grille - more accurately the other way around. Ford grilles have inserts that snap into the surround. You can snap the inserts out fairly easily using a hair dryer to heat the tabs to make them more pliable and then a flat blade screwdriver or similar. I'm not sure that would give you access to the bolt heads.
I wish i could remember cause I just changed grilles after an accident and I kept the broken surround - and I actually sold those 6 little bolts to another Ford guy, so I know I got access to them somehow. Sorry I can't be more help. As I think about it - you're guy may be right - we might have snapped the chrome surround off of its frame to get at those bolts. I just don't remember how and I've sold or trashed all the parts so I'e noting to refer to that might tell me. Really sorry man. Good luck.