"Employment with" vs. "employment at"

The typical distinction between the two options is that with with a company strongly implies that you work for them. Working at a company could imply that you are simply there doing work on their building or network or something like that:

I am working at Starbucks fixing their cash registers.

I work at Starbucks because they have free internet.

But this isn't a necessary distinction. Both work with and work at usually mean that you work for the company and, typically, people say "I work at Starbucks." With sounds a bit more formal to me and has a more "us" quality about it. At feels less formal and feels more like the company is disembodied or distant.