Plausible deniability

When I was visiting my new postdoc to get my ID and such, I was incredulous about the money thing. Several times I asked them, "My advisor and I agreed that I was moving and starting Sept 1. Should I change that plan since I am being paid starting July 1?" And they said that I did not have to change anything. At the end of our meeting, the admin asked what I was doing during the summer, and I said that I was at my current job through July. She asked if it was a problem for me to be paid by two sources, and I said that my current job wasn't government funds, so it shouldn't be. All she said was that I should check with my advisor to see whether I needed to do anything special given that I was being paid all summer.

I got an email from my advisor saying that I'm not being paid now, and I should say when I want to start working and being paid, so I asked the admin about the apparent discrepancy:

Finally, do you happen to know whether [advisor] has okayed paying me for July and August? His email below sounds a bit like he thought that I was registered for insurance, but not getting a stipend now. When I called him on Friday, I just left a message and didn't get a call back, so haven't yet been able to speak with him about this.

Her response:

I know he will provide the health insurance for you starting July 1st, but my understanding is that he can't pay your
stipend if you aren't here yet. If you could begin the Post Doc sooner than August 31st, we have the stipend to support you. But if you aren't here during July and August, then he can't pay you. Does this make sense? This was the concern I expressed to you last week.

Let me know what you and he decide about your start date. We can revise your letter to reflect the correct dates, if necessary.

That was not the concern that she expressed last week! In email she just has to cover her behind. I hate how outlandish it makes me sound, "You thought we would pay you when you weren't working? How ridiculous!"

Sometimes I feel like my life is stranger than everyone else's.

Update: I got back 1 month of the pay by arguing that during August I'm presenting at a few conferences, so it's relevant. And I got half an office at the main campus, instead of a room shared with 17 people. And after thinking so much about it, the total time that all took was 90 seconds.