Actually this is not true at all. The exact wording in MM3 is under the "Usage" sub-heading of the "Powers" heading. Usage says "A monster power is usable at will, oncer per encounter, or it recharges in certain circumstances."
There is then a paragraph for "Recharge", which states "Recharge: The power has a random chance of recharging during each round of combat. At the start of each of the monster's turns, roll a d6. If the roll is one of the die results shown in the power description, the monster regains the use of that power."
Since this is talking about A power specifically and how each individual power works it stands to reason this procedure is intended to apply individually to each one. NOWHERE in the rules is it ever stated or implied that there is a single monster-wide recharge roll, nor is there any example given of such that I'm aware of.
In all fairness its not 100% certain that the procedure applies to each power individually either, its an argument from context and WotC has been known to come out and issue rulings on things that differ from what context would suggest before, but the most consistent interpretation is its a per-power check.
The other reason to think it would be a per-power check is simply that there are a number of monsters that have several (sometimes even many) recharge powers. These are usually capstone solo class monsters with highly powerful recharge powers. Forcing them to recharge all of them on the spin of a single die puts a rather significant amount of the flow of the encounter on that single die roll. For most monsters it isn't a big deal and I think the DM should do it whichever way they find easiest (and maybe even roll for a whole group of identical monsters at once if it is simpler). For some solos though I don't think that is a great idea.
