The administrative search exception to the Fourth Amendment originally grew out of highly regulated businesses (e.g., food service), where inspection was made a condition of doing business. In contrast with a criminal investigation where individualized suspicion is required, administrative searches do not require individualized suspicion (e.g., every restaurant is subject to periodic health inspection, no matter how clean it looks.) Under current law, even where there is a significant law enforcement aspect to the inspection, you do not need a search warrant to conduct an administrative search.
If a health inspector is trying to trace the source of e. coli contamination, the inspector will attempt to determine sources of the contamination. In a rural area like this, an obvious possible source is a septic field. For the inspector to then investigate area properties, with a focus on those where there is excavation in the area of septic tanks or fields, is legitimate.
Similarly, although apparently not relevant in this specific case, if permitting is required before such excavation is allowed, a government inspector can investigate unauthorized investigation, cite the owner for excavating without a permit, and even get a court order prohibiting further work until a permit was properly obtained. And, of course, there would ordinarily be an inspection of the finished work. No warrants required.

