Yes, a fire is an NTSB incident and I would use that definition at a minimum unless the employer is more specific.
Historically, checking any such box would delay your eventual call for an interview. Not because they think you're a bad pilot, but rather because applications without such boxes checked are easier for the HR ladies to adjudicate. Not fair to you, but it's not supposed to be. It's supposed to save time and money for the company.
Such an incident will not be a problem at later stages of the process, where pilots are involved. You can often fast-track the usual process by meeting recruiters at job fairs or CP meet & greets (if available to you).
In this climate I doubt the incident box will delay you very much.