What you say is theoretically correct. However, be aware that real batteries have internal resistance, therefore the more current you draw from them, the more energy is lost. This means that if you double the current draw from a battery it will last LESS than half as long. This effect gets exponentially worse the faster you draw the current from the battery.
The mAh rating theoretically means that the battery can supply that much current for 1 hour (and theoretically can be scaled up and down proportionally with run-time and current draw).
So then...if the mAh rating varies then how do they come up with the rating? Well the rating displayed is for a certain time period. For lead-acid batteries, the rating is for 1 hour run-time (the battery will provide this many mAh if drained at a current such that it becomes empty in 1 hour). For most other batteries the it is the 10 hour rating that is displayed. (Although I believe either NiCds or NiMh have a 1 hour rating displayed, I don't remember but my guess is NiMh). So, yeah, that just means that if the run time you get is greater than 10 hours (or 1 hour) then the run time will actually be longer, and if the time you get is less than 10 hours (or 1 hour) the run time will be less...and the greater the time difference then the exponentially larger (or smaller) the run time.