I think battery-powered unintentional radiators can sometimes avoid testing, but battery-powered intentional radiators definitely don't. The statement about kits is also wrong, per pdabbadabba's comment below.
An intentional radiator module can get a module certification. In that case the final system still needs verification (the same kind of testing that an unintentional radiator gets), but doesn't need certification. When you see a label on the outer device that says "Contains FCC ID XXX-XXXX", that's the module's ID.
Verification is Declaration of Conformity (DOC)? You can either get a Declaration of Conformity from the lab or just sign it yourself. But in the chance you get audited and it doesn't function how you said it would then you'd get in trouble
Verification and DoC are different (and apply to different types of unintentional radiators), but you're correct that neither involves filing anything with the FCC (or any private body accredited by the FCC; for real most certifications go through a TCB, not directly to the FCC). You just make the file (including any test results required) and keep it in a drawer. The FCC can come and ask for it, and if you don't have it then you're in trouble.
ETA: And here's the section about battery-operated digital devices (i.e., unintentional radiators, with no radio transmitter):
> § 15.103 Exempted devices.
> [...]
> (h) Digital devices in which both the highest frequency generated and the highest frequency used are less than 1.705 MHz and which do not operate from the AC power lines or contain provisions for operation while connected to the AC power lines. Digital devices that include, or make provision for the use of, battery eliminators, AC adaptors or battery chargers which permit operation while charging or that connect to the AC power lines indirectly, obtaining their power through another device which is connected to the AC power lines, do not fall under this exemption.
And here's the section that makes it fine to build your own stuff in limited quantity, as long as you don't do anything obviously stupid:
> § 15.23 Home-built devices.
> (a) Equipment authorization is not required for devices that are not marketed, are not constructed from a kit, and are built in quantities of five or less for personal use.
> (b) It is recognized that the individual builder of home-built equipment may not possess the means to perform the measurements for determining compliance with the regulations. In this case, the builder is expected to employ good engineering practices to meet the specified technical standards to the greatest extent practicable. The provisions of §15.5 apply to this equipment.
An intentional radiator module can get a module certification. In that case the final system still needs verification (the same kind of testing that an unintentional radiator gets), but doesn't need certification. When you see a label on the outer device that says "Contains FCC ID XXX-XXXX", that's the module's ID.
https://apps.fcc.gov/oetcf/kdb/forms/FTSSearchResultPage.cfm...