I use LAX and have never needed a letter from anyone to get Employee Parking Lot (and rates)...we have had a base at LAX since 1999 (??) and I've only been based there for about 3 months during my time at Atlas. But even the time that I have been based in ANC, and JFK, I have never been asked to provide anything other than my company badge to buy a parking pass.
However, please don't get bogged down in this small-ticket item here...if you want the job, this is the small stuff. Consider the other benefits (or lack there of!!) of a career at Atlas...blah, blah, blah.