Soviet, and later Russian, doctrine in the event of a outbreak of a major war that is likely to lead to a nuclear exchange, limited or otherwise, includes using in-country (often undercover) or otherwise infiltrating Spetsnaz teams to attack strategic targets such as mobile ICBMs and cruise missiles. Naturally they assume that the US and its allies would try to do the same to them. Though in the current era and with the rather poor state of the various NATO special forces, they may be worrying a bit unnecessarily there.
EDIT: In addition they may also be worried about cluster munitions laid in ambush by cruise missiles and drones.
A rifle company or platoon being helicoptered or parachuted near a IRBM launch site a few hundred miles from the frontlines is rather different than what Listva's operators probably envision. For one, rifle platoons usually have automatic grenade launchers and anti-tank guided missiles.
"American proxies" based out of Dagestan using land mines to halt a convoy are a bit more concerning than the Green Berets, I'd imagine.
Given that the Russians had to reactivate two armored trains in an attempt to slow railroad attacks over the past couple of years in the Caucasus, it's also probably more realistic: The Chechens were allegedly downing Russian fighter-bombers with FIM-92s (they certainly had a few at least, as they showed them on TV) as late as 2000 or abouts, so it's also not entirely out of the question that some radical Islamist or secessionist group might try to attack a ICBM TEL just to get on TV or whatever. Naturally, instead of blaming this on crummy internal security and a weak government too busy fighting itself to fight its uppity feudal vassals, it's blamed on CIA.
Such are the dangers of having a plurality land mobile ICBM force in a country that cannot keep its criminals under control.
What stops someone from placing landmines on unpaved road?
Nothing. TELs operate on unpaved roads almost as a rule, obviously.
The MRAP drives ahead of the TEL and jams cellphone detonated IEDs like the kinds built by various insurgent groups the world over (such as Chechens and Iraqis). It locates the mines using magnetic induction and an EOD team dismounts to disarm and dispose of the bomb. It's similar to the US military's anti-mine weapons from Afghanistan, such as MAX POWER high power microwave and the STAR jammer, but combined into a single mine and bullet protected chassis.
It either finds a bomb and disarms it (or it explodes and disables the truck, but hopefully the crew survives) or it doesn't find a bomb because there isn't one there. It's designed for Russia's unique scenario where it's potentially operating mobile nuclear weapons in low intensity combat.
Which makes me wonder if they're more concerned about internal threats than Western SF.
I'd doubt the Russian security apparatus sees much of a difference, if any, between the two. If they were interested in stopping the Green Berets they'd need something to shoot down Javelins on their trucks, since the Green Berets like driving around in Humvees with FGM-148s out the wazoo.
There's probably no threat that exists between "Chechen/Dagestani artillery shell IED" and "loitering B-2 with Paveways" though.