I think you are overthinking this.
The 125A converter I have has a 15A 'style' plug in. You could plug it into a 15A receptacle, but if that receptacle is on a 15A circuit, the breaker will do it's job.
I have never measured the full load current on my converter, but just with the rules of electricity, it's got to consume more than 15A. I highly doubt that the converter company under engineered the cord.
I believe the converter receptacle in the RV looks like the typical 15A 'style' but it's rated to 20A [I could be wrong, I do not recall if it has the 15A/20A style]. Since the converter cord has a 15A style plug in and the receptacle can accept that 15A style plug in, I think I am more than good to handle 20A and be within code.
Of course, there are others here that know code more than me [which is probably everyone, since I am not an electrician], someone will chime in saying I'm just a butcher and I should be ignored.
I do feel comfortable that the entire circuit can handle a 20A load. The circuit is dedicated to one device too.