This is true for some cameras, but certainly not all. Many cameras, especially pro or pro-sumer grade, have non-linear ISO. That is, there are ranges for which it behaves linearly, but typically there will be some range - say the minimum up to 1600 or something - where it behaves as a linear range, and then the next setting up from that (where the settings are typically 1/3 stop) will reset to a lower snr. (And yes, that does imply that in such cases it often yields better results to go up by one or even two clicks in ISO)
I'm not sure if there any camera-phones that behave this way, though.