I'm not a satellite engineer, but I'd be surprised if this is true. What's preventing jamming a small, distant satellite signal with a big strong local transmitter?
It's trivially easy to jam GPS [0] and GPS is a much less complex signal than internet traffic.
[0] https://gizmodo.com/jamming-gps-signals-is-illegal-dangerous...
This is the castle and invader problem; the castle builders must guarantee that there is no hole anywhere in the castle, and the invaders only have to find or make one hole to render the castle useless. Whereas you could cut an underwater cable and guarantee outages for at least a few days or weeks, an adversary only needs to move to an un-jammed area in order to resume communication with the greater world.
Anti-radiation missiles which home on the strong local transmitter.
I'm not saying this flippantly. Obviously not all Starlink consumers have access to such a thing. The scenario I'm talking about here is when a country is trying to choke the military communications of an other one.
The big benefit of these LEO satellite constellations is that they have hundreds of satellites in them which makes anti-sat weaponry not cost effective. (Or at least that's the hope.)
For more localized conflicts this is also already routine, lots of countries in civil war order ISPs under their jurisdiction to start blocking websites or the entire Internet whenever blocking it benefits the incumbents (which is always).
In any case there are counter-measures and counter-counter-measures for such situations. It's why Starlink has always been presumed to be a financial success even if civilians don't get behind it; every government in the world (and especially the DoD) would want a satellite network that can provide Internet connectivity to any part of the world, and you would have to literally shoot down dozens of satellites to impact its availability.