In the interest of full-disclosure, I am a former firefighter, but I was mainly focused on structural firefighting. We did respond to wildland / brush fires, but only got involved in direct suppression activities on the smaller fires. Larger wildfires we just provided protection for exposed structures and let the Forestry Service handle the primary suppression efforts. Anyway...
One of the main dangers of wildland fires involves something called the "wildland / urban interface"[2]. This is where homes and urban construction border on and/or intermingle with wildland areas. When you hear about "Wildfire X destroyed N homes" this is usually referring to events that happen in the WUI. I don't think it's hard to see how dropping bombs in this area could be problematic - even using the specially tuned bombs referred to in the article.
Also, a wildland fire isn't like an oil-well fire in that you don't have all the fire concentrated in one small, well-defined area, where you can quickly "snuff" it out. In a wildland fire - especially in the driest, most dangerous conditions - it seems likely to me that the same shockwave that snuffs out flames in a certain area, might well spread embers that actually spread the fire to an even larger area.
Maybe there's something to this, but overall I'm somewhat skeptical.
[1]: https://en.wikipedia.org/wiki/Oil_well_fire
[2]: https://en.wikipedia.org/wiki/Wildland%E2%80%93urban_interfa...