Proper use of "we" in this conversation

Is the following use of "we" in an informal conversation incorrect or ambiguous:

Mary: How did your day go at work?

John: It was good. I had a meeting early in the morning and we had lunch with Jack to discuss the project...

Mary: Who's we?

John: Me and Jack.

The alternative would be for John to say: "I had a meeting in the morning and I had lunch with Jack to discuss the project".

A native speaker would not say 'we had lunch with Jack' if the only people having lunch were the speaker and Jack. The word 'we' means that there was at least one more person having lunch.

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