> Why would the base state be "No cryptography, no communication, no information" and not "No cryptography, communication, information?"

Because you treated cryptography as a field in its entirety. I think in practise that is how cryptography as a field works normally. Most secret messages communicated with crypto simply wouldn't be communicated (or just communicated in person) without the availibility of cryptography.

Even if the alternative is communicating in a way open to evesdropping i think there is still an intent requirement.

> Exactly at which point does the lie happen?

When there is intentionality to mislead (including by omission).

If you want to be really nitpicky, the definition i would give would be:

Taking (or failing to take) some action for the purpose of causing an adversary to have incorrect or incomplete beliefs that benefit you.