The issue with stiffening is as followes:
If you have a barrel Fluted and a non-fluted barrel OF THE SAME WEIGHT (thats the key) the fluted barrel will be stiffer.
Now critics of fluting will say for example that fluting a 16" hbar will make the barrel less stiff. This is true when you compare it to a regular 16" Hbar, but it a bad comparison. Naturally the barrel with more mass will be stiffer.
Overall, as long as it is done right, the advantages to Fluting out weight that (very) minor consequence. As mentioned before, most precision sniper rifles ($10,000+) are fluted.
I ordered my 16" hbar from bushmaster pre fluted, and I couldn't be happier with it.
Here is an excerpt from their website:
Fluting (machining lengthwise grooves into the outer surface of the barrel) increases the surface area of the barrel - thereby allowing increased radiational cooling of the barrel mass. This process also adds to the "stiffness" of the barrel which enhances its accuracy. A third benefit of fluting is that the barrel is lighter after machining removes the steel in those lengthwise grooves. A fluted barrel will last longer, shoot straighter, and is considerably lighter than a standard heavy barrel. The accuracy gains would be most noticeable at longer distances or to the competition shooter, but for only $50 additional for most Bushmaster barrels, many feel that the benefits of fluting are well worth the cost.