First off, you need to learn the 'grammar' before you try parsing sentences
UL never 'approves' anything. List, classify, recognize: yes. Approve, rate, pass: no. It's an important distinction for them.
Second, UL is not the only game in town. For fire sprinklers in particuler, FM has just as important a role. That's just in 'market' terms; from a legal perspective, it is improper for any law (or code, regulation, etc.) to direct you to do business with any particular private business. Thus, and "NRTL" will do. In the past decade hundreds such operations have popped up.
There's a world of difference between NFPA 13-D (dwellings) and 13-R (residential). You really need to appreciate the distinction; the two are as different as cheese and chalk.
13-R is a simply an elaboration on the basic sprinkler code NFPA-13. It does not change or ease any of the 'industrial' requirements.. 13-R was meant for application to places like hotels, high-rise condos, and other places of mass accomodation. The basic requirement of NFPA-13 that fire pumps be listed for that specific use, and all the unique power requirements, apply. So do the alarm and piping requirements.
13-D is a completely different animal. Intended for small stand-alone houses, it has very few requirements. I suspect that any sort of pump, wired like any other appliance, would be perfectly fine. 13-D systems don't need flow alarms, and can share the same piping as the household appliances. You can even use ordinary PEX plastic tubing.
So, it's critical that you determine which standard applies - then get a copy and read it. When the inspector asks a question, refer to the standard. Reading between the lines, it sounds like you are dealing with someone who does not appreciate the revolutionary differences contained in 13-D.