He's saying don't unplug the battery, you'll just start from scratch again. And it's not the CAIs fault, if it were making problems you could conceivably end up with a failed monitor (though I can't think of one affected by intake/MAF/intake air temp stuff), but it wouldn't by itself prevent the PCM/ECU from running the monitors when the test conditions are met. Do you know which ones aren't running/passing? Kind of an important bit of info there. I'm sure there is a Ford published guideline for getting a car to go through all the monitors but I haven't seen it. I think it's totally plausible you could drive 160 miles and not meet all the test conditions for all the monitors, for instance the weird one Whynot mentioned above.
That said, if before this you've been driving the car for months on end and ended up with some monitors not ready/not run, that's fishy. Some test conditions are a little out of the ordinary, but they should definitely all run over a period of time like that.
Is it possible your car has an aftermarket tune? Cause this could prevent some monitors from running, for instance the tune on my car does not make the PCM monitor o2 sensors and I've never had a CEL for that (even though the rear one is totally unplugged and obviously not doing anything) and for awhile I had a vacuum leak with an EVAP line going into the intake manifold and this also never triggered a CEL (the end result of any monitor repeatedly not passing).
Makes me wish I'd paid a little more attention in my class about emissions.