tl;dr - Parallax is.
The Genesis, SNES, and PCE were made with the hardware capability, from the core system, to reposition any part of the screen at a different scroll point (to divide the screen into different scrolling speeds and direction). That by definition, is hardware assisted parallax. The PCE uses the traditional Hsync interrupt, the Genesis uses scroll ram, and the SNES uses HDMA. They all do the same thing. The Genesis has an addition BG layer allowing for more complex parallax, and the SNES can have up to 3 layers (4 in limited color modes) for even more advance parallax layering.
All these systems are capable of parallax. All these systems do parallax at some level of functionality when the developers make that choice. There is hardware assisting with the parallax in these consoles. There is no "fake" parallax in comparison from one to another, or better said is that they are all fake parallax - but some methods more advance than others. Even software parallax isn't fake. If you see a parallax effect, then it's parallax. The only thing to say about it, is the level of complexity accomplished for the effect. Using sprites, using dynamic tiles, using hsync interrupts, using whatever means necessary - none of that makes it fake.
If parallax is created through palette animation, then it's still parallax. If parallax is created through sprites for star fields, then it's still parallax. If a screen is split into "paper scrolls" (scrolling parts that don't overlap one another), then it's still parallax. Etc.