Bug free software means developers would not disclose any information about present bugs in the software they ship to customers.

Really bug free commercial software does not exist. And can't exist. There are always bugs which are known but would not be fixed.

To have no bugs, which is extremely unlikely for a program of any real complexity. Having bugs, and being functional, are fairly self-explanatory and independent of each other. No need to try to conflate them.

Not sure what your quote is supposed to mean. That's a textbook example of someone who doesn't understand software at all making laughable requests of their engineers.

To be bug free we must be able to define what a bug is. So, what is a bug?

The reason for that quote is from what you have said a bug would be anything you didn't expect, even if it is consistent or not with the specification as that merely affects if we classify it as functional or not (a classification I profoundly disagree with, obviously). It is simply a negative rephrasing of what the marketing guy said and laughable in the same way.

As another commenter pointed out,

> One plausible definition is “system deviates from its specification”

And that's quite reasonable. So I actually retract my argument.

For my own definition, I was considering a bug to be any behavior that the software engineers weren't expecting. Because those can exist invisibly for a long time until they become so bad they become visible. They can also exist for decades without causing any problems to functionality at all.