This always happens because mathematicians and computer scientists use shorthand descriptions that elide the details for ease of conversation. It's no different

This always happens because mathematicians and computer scientists use shorthand descriptions that elide the details for ease of conversation. It's no different than saying that you're "multiplying by dx on both sides". "Is the traveling salesman problem NP-hard?" is talking about family of problems, not specifically an instance of it. If you fix the specific graph, then obviously it's not NP-hard since there's no N. It's so trivially obvious when you know this that it isn't worth talking about. It is also completely unreachable for many people who don't know what these terms mean. I have, in the past, had a misconception of this shape in a different field. In my case, it was my belief in DNA as code that is executed by things that message-pass between each other sometimes directly through the substrate and sometimes by modifying the DNA. Overall, this isn't a useless model but I needed to know when to not get addicted to it. To biologists with mathematical backgrounds, it's obviously wrong to just take the TM execution of DNA as a model. To me, it was less so. So it's just unfamiliarity with the basics.