There was a "warning" of sorts in the owners manual, at least for the 91-94 Explorers, to only use all-terrain tires since all-season or "sport" tires would have too much traction and allow the vehicle to tip over easier when cornering if going too fast. All-terrain tires do usually have less grip on pavement due to the tread, so I guess Ford's hope was this would minimize the risk of the top-heavy SUV design. Obviously, the use of low-quality all-terrain tires and low tire presure was more of a problem than anything else.
As mentioned above, some tire retailers have declined to install any size tire other than what the vehicle was originally equipped with, and cite the Firestone incident as the reason, and this may actually be company policy, either with regards to Explorers or all vehicles in general.
However, it's pretty out there for a tire tech to decline to install a tire based on the type, and even more so since Ford started equipping Explorers with the Michelin Cross-Terrain SUV, an all-season tire that was the predecessor to the LTX M/S 2.
The original Michelin LTX M/S, Cross Terrain SUV, and plenty of other all-season tires were also Ford and Firestone-approved replacements under the replacement program for the tire recall.
So, the tire tech is incorrect. I'd say you should speak to the manager about this and have the tech educated about what the correct information is. In some ways it's good that he's concerned enough about safety that he wants to follow guidelines, but he needs to follow the actual guidelines, not misunderstood ones. Hopefully the manager will apologize for the mistake and install the tires for free or give you some kind of a discount for the hassle.
If you're unable to resolve the issue at the store, I'd suggest calling the store owner, or the office of the company if it's a chain store. If you're still uable to resolve the issue, you may just need to take your business elsewhere. There are still plenty of tire shops that will install whatever type and size of tire you want on your vehicle.