I don't think you interpreted the sentence in question differently, just the nature of how it is being translated into a query. They're talking specifically of how to translate into a query over a quantified relational algebra. Relational algebra always operates on and return sets. I'm pretty sure the author here is still looking for a boolean, but you can't ask a relational query engine does a result exist? You can only get back sets. The further question of whether or not the set is nonempty is an extra feature probably built into most real-world implementations of query engines, but it's not part of relational algebra.
The actual problem they're identifying here is that of deciding how or whether to turn 'a' into a quantifier. Do we have 'any' would be less ambiguous, definitely an existential quantifier. Do we have 'a' depends on context, as it could mean one specific person and not be a quantifier at all, but I actually still disagree with the author here. I think they're right that English-speaking humans will unambiguously understand 'a' in this context to be a quantifier, but given that is possible at all, I don't see why a large language model can't. If it was actually being used to specify one person, the additional context would be in the sentence itself, as in 'do we have a reporter named X' or something like that. Given there is no additional qualification in the sentence, I'm pretty sure existing large language models can easily figure out what it means, and the only case in which they'd be wrong is if there were additional context outside of the sentence, but a human would be wrong too if all they heard was the sentence.
The actual problem they're identifying here is that of deciding how or whether to turn 'a' into a quantifier. Do we have 'any' would be less ambiguous, definitely an existential quantifier. Do we have 'a' depends on context, as it could mean one specific person and not be a quantifier at all, but I actually still disagree with the author here. I think they're right that English-speaking humans will unambiguously understand 'a' in this context to be a quantifier, but given that is possible at all, I don't see why a large language model can't. If it was actually being used to specify one person, the additional context would be in the sentence itself, as in 'do we have a reporter named X' or something like that. Given there is no additional qualification in the sentence, I'm pretty sure existing large language models can easily figure out what it means, and the only case in which they'd be wrong is if there were additional context outside of the sentence, but a human would be wrong too if all they heard was the sentence.