I've done it myself. I took a picture with the following configuration and the pictures were identical.
Canon 7d with 18-135mm lens at 35mm.
Canon Rebel (film, so full frame) with 35-80mm lens at 35mm.
Why did the picture turn out the exact same? Because the 18-135mm at 35mm is at 35mm on my 7D. Since this is an APS-C only lens, the stated focal length is correct. It was not "zoomed" in to 56mm. The picture was IDENTICAL to the Canon film Rebel at 35mm.
Do it yourself and be amazed.
Get an APS-C-only lens and sent it to XYmm on a crop body. Then, get a EF lens and set it to the same XYmm on a full frame body and the two images will be the same. (I understand that the image will be different if an EF lens at the same focal length will be different when put on an APS-C body). Trust me, do exactly what I said and you will see that I am correct.
Do it right now and report back.
I don't know what to say, but you're the only person who's experiencing this. Everything everyone else is writing is both consistent and correct (even if there are arguments over semantics relating to focal length not being an absolute measure of field of view).
I had a 17-55mm on my t2i and a 17-40mm on my 5D III. Used both very frequently at 17mm.
One of them was a lot wider.
I'm sorry to be so blunt, but you're wrong. "Equivalent" doesn't mean the focal lengths are mis-marked and 35mm on the EF-S lens is the same as 35mm on the EF lens exactly; what equivalent means is it's the equivalent field of view in terms of what 135 film or a FF sensor would see.
If this were true, the 10-22mm would be the widest Canon lens available for any dSLR. But the 14mm f2.8 is wider on FF than the 10mm is on a crop body.
All focal length means is the distance from the focal plane at which the lens's optical center focuses at infinity. That distance and the size of the sensor determines the field of view.