The law was specifically written to exclude things like independent power sources and backup generators etc...

From 42 U.S.C. § 7651a(17)(A) [1] which defines the power generation units that are covered by the law:

"(17) (A)The term “utility unit” means— (i)a unit that serves a generator in any State that produces electricity for sale, or (ii)a unit that, during 1985, served a generator in any State that produced electricity for sale."

The key phrasing there is "for sale". The clarification from the EPA simply restated that these units don't fall under the regulatory authority because under a plain reading of the law, they are not generating power for sale. [2]

The EPA certainly cites Trump's power agenda several times, but that doesn't make the plain text interpretation of the law wrong.

[1] https://www.law.cornell.edu/uscode/text/42/7411

[2] https://www.epa.gov/newsreleases/epa-issues-permitting-guida...