I think SpaceX's concern is more related to domestic liability. The US's policy has been that they will not provide offensive aid for attacking into Russia. They've been very careful about the range of the systems they send for that reason.
Unrestricted Starlink is not subject to those range limits. So, if the attacks which went deep into Russian territory involved Starlink mounted to drones, it would essentially be in violation of the US's own stated policy about military aid to Ukraine. Thus far this hasn't caused any trouble, but if something were to happen (eg an escalation), SpaceX might get thrown under the bus by the US government since they aren't contracted by the DoD to provide such service.