You are somewhat correct. The door switch backlighting does not dim with the dash lighting. Its actually a separate circuit that does not dim at all. Even with the factory lighting, if you dim the dash lights all the way down, the door switch lights will stay their full brightness (which isn't really very bright to begin with).
So yes you will not be able to dim them. But as far as wiring it to the wrong circuit, you probably have the right circuit but didn't realize that they do not dim. If they light up as soon as you turn the ignition switch on, then you do have them wired wrong. They should turn off and on with the headlights just like the dash lighting. The only difference is they do not work with the dimmer on the headlight switch.
To prove this, check your fuse panel. The dash lights are on a fuse labeled "illum", and the door switch lighting is on the fuse labeled "int park".