I think people have looked into it and produced the most likely explanation. The name plate thing is a fun kind of 'folk etymology' theory but isn't supported by any evidence at all beside the hunches of people who've been around boilers. The other variant has a wealth of evidence supporting it.
Boilerplate's early use was referring to boiler material, but it likely got semantically mixed together with the term for "standard form plate affixed to a boiler", as this term is actually more from the legal industry where it's literally a document with blanks you fill out, which more closely fits this definition.