"Your call is very important to us," is not a true statement either. The truth is self-evident.
"I promise I'll tell the manager about this," is of course not a real promise either. It might be uttered with good intent, or might be designed to get an annoying customer to go away, but still...
You can already guess the problem with little lies. They blur the line, and they lead (pretty quickly) to big lies. The worst kind of little lies are the ones you make to yourself. Once you're willing to lie to yourself, you're also willing to cheat at
Companies that refuse to break small promises have a much easier time keeping big promises. And they earn a reputation, one that makes their handshake worth more.
Given that expectation and trust are just about all we have left to sell, it seems to me that little lies and small promises are at the very heart of the matter. And they're a simple choice, nothing requiring an MBA or a spreadsheet.
It all depends on what you want to stand for.