You raise and interesting question: it highlights an important distinction between what is acceptable in informally spoken or perhaps even ‘tweated’ English and what is acceptable in written English, and indeed in spoken English, other than where the speech is an off the cuff response to a question, as in this case.
I should be shocked to read this casual usage in thE NY Times except as a quotation, as in your case.
In effect, Lara has substituted the conjunction ‘and’ for the subordinating conjunction ‘to’. We all know Lara is trying to say something that makes sense (grammatically, at least). It is obvious that It is the infinitive that is intended. We are used to this colloquialism and understand what she is saying.
Some may even sneer at her lack of education, but that would be unfair. This was off the cuff under pressure. As such, it is a very common colloquialism. It is so familiar that we do not even have to think about it.
If we did, we should see that grammatical analysis breaks down.
They don’t try and they don’t stop a loser.
This is nonsense, of course. Moreover, ‘try and stop can only work in the future or the imperative. You cannot say
They tried and stopped the burglar but he got away.
But the burglar could say
Just you try and stop me and see what happens.