That is very scary rhetoric. We know that Russia has effective anti-satellite weapons. A small number of them could effectively end the usefulness of LEO for everyone. Such an action would of course damage Russia as well. But Putin is not a rational actor.
More likely, Russia could take out one Starlink sat and then say that if SpaceX does not shut down Starlink service in Ukraine they will take out more. There is no defense against that kind of blackmail.
Putin has already demonstrated that he doesn’t care about global opinion based on his crazy nuclear weapons threats and horrific attacks on Ukrainian civilians. His only real allies are Iran, Belarus, and North Korea. Even China is keeping its distance; nominally the Chinese are offering support but they have not voted with Russia on key UN resolutions, instead choosing to abstain. That speaks volumes. The Chinese do not want to see global economic disruptions.