That's still an oversimplification. POST only implies that the request is NOT idempotent, and that the request body is submitted to the origin server for "processing". Consider for example, resources that search for other resources via information in the request body and redirect to them. There's nothing wrong with this pattern, and in fact it works nicely for rapidly-changing server-side information since caching the result of a POST is not allowed.
The core problem in my mind, is not whether one should insert or update on PUT/POST, but whether one should even be considering HTTP-based APIs to be gateways to what amounts to a database. The domain concepts in the application might not map directly to a resource-centric design, and that's ok. When you focus on the resources, their behavior, and hypermedia, then you "get" REST. If your application isn't shaped like HTTP/REST, then maybe it shouldn't try to be.
The core problem in my mind, is not whether one should insert or update on PUT/POST, but whether one should even be considering HTTP-based APIs to be gateways to what amounts to a database. The domain concepts in the application might not map directly to a resource-centric design, and that's ok. When you focus on the resources, their behavior, and hypermedia, then you "get" REST. If your application isn't shaped like HTTP/REST, then maybe it shouldn't try to be.