"If State A caused the launch to happen, then State A is fully liable for damages that result from that space object."
and
"Whereas under most national legal systems an individual or a corporation may bring a lawsuit against another individual or another corporation, under the Liability Convention claims must be brought on the state level only."
Liability was a lot clearer there - it was a Russian government satellite, launched by the Russians.
Here we've got a satellite owned by an American company launched by an Indian rocket. The US is likely to say "the Indians shouldn't have launched it!" India's likely to say "it's an American satellite!"
"If State A caused the launch to happen, then State A is fully liable for damages that result from that space object."
and
"Whereas under most national legal systems an individual or a corporation may bring a lawsuit against another individual or another corporation, under the Liability Convention claims must be brought on the state level only."