This doesn't mean that the assertion is wrong, but the data provided seems less relevant than one might hope.
I'll also note that as an EV owner, when I bought a home charger I didn't even consider a rapid charger, because I don't need it -- charging at medium speed is just fine. In retrospect I could have done OK with a standard outlet and slow charge, but the thousand or so it cost me for the charger and installation was worth it for convenience. I think I'm the norm. That would mean the graph showing high prices for rapid charge at home is not terribly important -- the key metrics will always be standard charge vs. petrol for at home charging.