This is not true, or at least it is not that simple.

The highest capacity AA NiMH out there is rated at around 2800 mAh, but those have given up everything else in the name of peak capacity. For many people, the Eneloops are the best NiMH cells out there right now, and their capacity is around 2000 mAh (but their low self discharge rate makes up for it.)

As for alkalines, here's the spec sheet for the Energizer E91 alkaline AA, a fairly typical name brand AA alkaline. It delivers pretty close to 2800 mAh if discharged at a low rate.

However, here's where it's not so simple -- NiMH cells handle higher discharge rates better. If you discharge an alkaline at a high discharge rate, it's capacity goes way down. For example, that alkaline only puts out about 1500 mAh if discharged at 500 mA, when the NiMH cell will not lose much capacity at all due to that higher discharge rate.

For a low discharge rate application, an alkaline will last longer. Such applications include smoke alarms, bicycle tail lights, TV remote controls, etc.

For a higher discharge rate application, NiMH cells (especially LSD cells like the Eneloops) will last longer. This includes power tools, high power (> 1 constant watt) bicycle lights with AA cells, etc.

Of course, considering that NiMH cells can be recharged and alkalines shouldn't be -- NiMH cells are the winner for most applications nowadays. (Well, lipo or lithium ion cells tend to do even better, but that's another discussion.) But it's not quite accurate to say that NiMH cells have 4x the capacity of a good alkaline.