Yeah, many trailer mfg offer the LT as a upgrade option.
In fact Carriage Domani at 11500 lbs offered a 20" P tire as a option.
I personally have no problems getting a ST or P or LT tires for any of my trailers with a full warranty with the dealer and mfg blessing.
Now if I had a agenda or was a complete newby and backed a dealer/manufacturer into the legal liability corner of a particular question like "I want to replace a 3500 lbs rated ST tire with a 3042 lb LT tire" then they would have to say no.
Some folks have a agenda of scaring others away from a particular brand or tire with the old legal liability lawyer talk. Nothing new there.
Other folks are more interested in recommending the "best options" possible for a member asking for tire help.