'Exhaustive'? They may have been exhaust ing (!) but can you really ever search exhaustively for a species?
As for whether it's possible, I would say yes. Environmental DNA (eDNA) sampling can be used to see if a particular species is present even if you don't visually or audibly observe the species:
> eDNA is increasingly being used for biosurveillance, species occupancy studies, and the detection of endangered and invasive species, particularly in aquatic ecosystems [0]
There's a very recent paper that has demonstrated that animal DNA can be obtained from the air and used to identify animals present in a given space. [0]
> Clare set up vacuum pumps with filters in 20 locations in Hamerton Zoo Park and let each run for 30 minutes. [...] The team identified 17 species kept at the zoo and others living near and around it, such as hedgehogs and deer. Some zoo animal DNA was found nearly 300 meters from the animals' enclosures. She also detected airborne DNA likely from the meat of chicken, pig, cow, and horse fed to captive predators indoors. [1]
In the near future we'll probably see fairly widespread use of this kind of tech in the search for rare and evasive species.
[0] : https://peerj.com/articles/11030/
[1] : https://www.science.org/news/2021/07/dna-pulled-thin-air-ide...