I understand everything but that. My first thought was that it was because he had just gotten back from California and hadn't bought any groceries yet, but in that case, why is it full when he shows it to Caselle?
Caselle answers your Q in the film; he says something like, "Maybe this is for my benefit. Maybe I'm not supposed to believe you. Maybe they want you playing this all alone."
Seems a bit implausible to me. How long is it between Stillwell meeting Caselle and the two of them getting to his apartment -- an hour or two? That's an awfully small window for a) one of the Major's agents to find out Stillwell has hired a detective, b) that agent to communicate that to the Major, c) the Major to suggest filling up Stillwell's fridge as a way of making him look crazy, d) the agent buying a whole fridge's worth of food, e) the agent breaking into Stillwell's apartment, f) the agent arranging all the food in the fridge, and g) the agent getting out of there undetected, without leaving any sign that the apartment had been broken into.
I mean, I realize on some level the whole movie is implausible, but most of it seems more logistically believable. Also, maybe I'm forgetting, but was there any indication that someone spotted Stillwell and Caselle together that early on?
Before Stillwell hired the detective, he's already been observed as acting erratically, and was probably tailed to the psychatrist and then the detective. The Major had plenty of time to arrange for groceries to be ready to fill the fridge.
And remember that Willard (George Kennedy) is following them (that's the reason why Caselle believes Stillwell) so they know that Stillwell has gone to see a detective and have time to fill the fridge and so...