let’s dissect this a little.( disclaimer I did not learn the Mesilas Yeshorim, I only based this on what you wrote)
1 if there is a real danger then the fear is proper and we do not say that he is lacking in bitachon ( although he still needs bitachon in his situation as well)
2 an irrational fear has no place and it antidote is bitachon
Now let’s go to our hypothetical case, the original episode is very rational and a ligitamate reason for anxiety the only problem is the association and unresolved fear/trauma that is causing the anxiety, so saying bitachon iin the straight forward sense is maybe incorrect in this case, although one would need bitachon it would not only be in trusting hashem but also require many steps in resolving the fear/trauma and association.
Also many anxieties are issue with people making it much more complicated, and requires lots of proper actions