Thanks for the responses, cornflake, amergina, and veinglory. I have a follow-up question:
Is it weird for a publisher to make this type of request before looking at the full manuscript? Isn't this the type of change that would normally be worked out in the editing process?
SIDE NOTE: The more I look through my manuscript for trademarked names, the more it dawns on me how this request undermines the authenticity of my story. I did a lot of research into what type of gun or airplane would be needed for a required task, but those are trademarked names, which means I would need to discard the fruits of that research, in favor of fictional makes/models.
My understanding is that it is unusual. Do you know of others who have successfully used this publisher? And if so, can you talk with them. This request sounds out of left field.
Just saw the followup message by OP.
That's quite sad. Seems they are a publishing service and have no idea how copyright/trademark works. If it were as they stated, no opinion piece anywhere (blog, newspaper, etc) would ever be able to mention any product or service for any reason. Worse off, just saying/writing the word "apple," a generic fruit, could leave them open to someone alleging they meant the company Apple, and thus trademark infringement. Wouldn't be able to say Kleenex though its the common word now for handkerchief, etc. and so on. So many words wouldn't be mentioned just because of potential fear of confusion.
As stated above, trademark is to avoid market confusion surrounding products and services. Remember, Apple tried making the letter "i" trademarked to them on all products and mentions anywhere, and they were told to take a hike.
You did the right thing, OP. Walk on. Best of luck.