They're right.
I've seen collars/sleeves to reduce headtubes internal diameter (which mean you can use a 1" non-integrated headset and 1" steerer in a 1 1/8" headtube), but if you are looking for a solution for an 1 1/8 integrated headset that won't work. If integrated, I suspect you would have to have the steerer made bigger (sleeved) or find bearings with the o/d for the frame cups and i/d to suit the steerer.
To be honest, as there is no easily commercially-available solution, unless there was a very good reason to persevere I would just get a 1 1/8 fork....
Edit: Having thought about it, the internal headtube collars might work to reduce the I/d of the bearings. iirc SJS stock them; might be worth giving them a call and discussing?