Yeah, but doctors also don't tell people "you have bacteria" or claim "we found a cure for bacteria". The lack of nuance on average is largely due to a lack of nuance from experts. The media treats cancer as one big thing and bacteria and viruses as separate things. Thus the average joe inherits 'treating cancer as one big thing' from the media.
But yeah, oncologists aren’t telling people “you have cancer” the way they might say “you have MRSA”.
Honestly, I think people probably get false impressions because cancer usually hits old people and old people are, frankly, often not reliable narrators.