LEO also does lots of things without asking the FCC, but I'm not personally aware of any using any sort of jamming technique, nor have I fielded a request for such a thing. They're much more interested in getting and keeping their own mobile communications working properly than in figuring out how to make someone else's somehow not work. (And yes, bog-standard cell phones are part of their kit, so they're not going to be jamming those.)
Citation: I work with public safety communication systems, including with departments that have SWAT and bomb squads.
Here's what happens in reality whenever something nasty is going down: The cell network collapses under the weight of its subscriber base and becomes unusable. This causes text messages to be delayed by minutes or hours or just fail to send, TCP connections to hang forever, and phone calls to quickly drop or just fail to connect.
This may appear to the less-clued end-user as a DoS attack, ala "jamming," especially after spinning it through the Facebook Stupidity Multiplier in the rundown after a noted event. But it's really just a lack of service, not a denial of it.
Last year I was grocery shopping when the local tornado sirens went off. I pulled out my pocket computer to get a radar map to see what my options were and plainly wasn't the only person trying to do this; despite having awesome 4G capacity just minutes prior, and still having plenty of signal strength during, what normally took seconds took at least 5 minutes. (Thankfully, there was no actual tornado, and my SO was able to successfully send word to the kids at home to stop watching Youtube and get to the basement in fairly short order.)
I could tell from the morbid disdain on the faces of those around me as they stared at their own temporarily-useless phones that I wasn't the only one who was experiencing this issue.
Government conspiracy? Active jamming before rounding up devices to hide The Truth? No. Just an oversubscribed, under-built network performing as best as it can at a time when everyone wants to use it Right Now.
Doesn't matter if it's a bomb threat, a riot, a huge fire, a natural disaster, or any other source of immediate public concern -- the network doesn't care what is happening, it is simply aware that it can't keep up. And it is affected by this of this in far less time it would take for any domestic government agency to start jamming. (What would they jam, anyway, to cause a criminal's 2-way radio to cease functioning? Everything/wholesale broadband RFI? Then their own stuff wouldn't work.)