I'm not aware of any mandatory certification requirements for appliance techs in the U.S., but nowadays, there is a lot of very good training info available if someone really wants to learn appliance service.
Here in my state, the appliance techs can generally work on any related electrical, gas, water or refrigerant [with EPA 608 Cert.] within the appliance itself, but nothing external beyond the electrical cord cap, water or gas line without the proper respective state licensing.
Most techs will probably connect a saddle valve to the homes cold-water branch piping for a refrigerator icemaker water supply line, but even that may be considered as pushing the boundaries, since the potable water system is involved.
I think that the repair company's invoice is normally the only evidence you would usually have to indicate that anyone "reputable" had serviced the equipment.
If there's no record of the service because the homeowner hired some fly-by-night repairman to do the work and paid in cash, then that's where law enforcement may need to get involved to track him down, certainly if someone was injured or killed as a result of his work.
On a related note, these days, with so many different appliance brands and models, each with their own specialized electronics and servicing techniques along with DIY internet competition and the need to stock many expensive, brand specific replacement parts, service tools and equipment, it's very difficult to turn a profit in appliance service, unless your connected with a large, high volume regional or national service outfit. Add to this the lower cost of replacing appliances versus repairing things like window AC's and the profit of non-warranty repairs disappears completely.
This is mainly why I no longer offer any appliance repair service for other than immediate family members.
All I can say is… all of my own household appliances and HVACR equipment work fine… and I don't miss the endless circle-jerk associated with that type of work at all.
