China was doing similar with sanitizer trucks running up and down streets so it's not terribly unfounded--actually that fake news is likely better than >99% of the actual crap on there.
[0] https://www.clarke.com/blog/aerial-mosquito-control-applicat...
Edit: footage of the trucks because they're neat https://futurism.com/neoscope/watch-china-spray-entire-city-...
No idea what the efficacy is.
The NY health department does use helicopters to drop larvicide on likely mosquito spawning grounds[1]. Your mom did believe a false story and also there absolutely was (and is) a plan to use helicopters to distribute an an anti-disease treatments over NYC.
I think the tricky part of the misinformation we are all dealing with is that many elements of it (method of distribution, the idea of spraying down a city) are things that are happening in some way - the false narrative is the particular combination people believe in. I think it's part of why flat denials are often ineffective.
[1] https://www1.nyc.gov/site/doh/health/health-topics/west-nile...