Yep I agree with you, within the world of guitars. The history of the word Tremolo in reference to pitch modulation goes back many hundreds of years in the world of classical music, whereas the guitar and amp derived meanings are only about 70 years old. Look up the wikipedia article on tremolo and the various definitions are listed in the first paragraph.
Add to that the people who named the Vibraphone, which does not produce vibrato at all, and you can see the two terms are used interchangeably, as it says in the first paragraph of your image. The vibraphone preceded Fender's amps by more than a decade, and was a staple in Jazz, one of Fender's target audiences, so it's not a stretch to say that the Vibrato channel on Fender amps was marketed towards these jazz guys who liked the effect of a vibraphone, since it produced the exact same effect.
Everyone likes to shit on LF saying he was such an idiot for mixing up the terms, that tremolo is a volume modulation, but they are missing the bigger picture, which is that in their own way, everyone is an idiot.
My hot take