Yes, that's true.
If you have checked all the above then there is not much more you can do.
The correct mounting is important, it should be cushioned on rubber bits, not screwed tight to the floor. The floor can amplify the noise.
If the pipes are quite stiff and lie on the floor, that can also make it noisy.
If you don't have an accumulator fitted I would suggest you consider it, it will smooth out the flow and stop any rapid switching off/on, and pulsing of the water.
That was the problem with ours (a FloJet pump) and it made a terrible racket every time it switched.
Sometimes "progress" is not all it's cracked up to be!