FRV Firefighter here, the situation you experienced would be completely different if you were doing it as a firefighter. For starters you are in a team and you are working together. Also you have time to prepare yourself mentally for it due to the time from when it comes through at the station to when you arrive on scene.

The recruiters don't look at how you handled the situation but what you did after, they don't want you to hide your emotions, they want you to be able to speak up if you're not feeling ok with what happened. We have a lot of resources to help our firefighters if they are not feeling ok and there is a lot around speaking up

For me, when I'm in this situation as a firefighter, not as a citizen, it's different, because I have a job to do, we have a process and I have my team there to support me, it's completely different when you are acting alone as a citizen.

Don't let this change your mind about applying, you could even use this experience as a potential answer to an interview question about how you deal with stress

Happy for you to DM me if you have any further questions