This is just false. The only time this example is mentioned in that ruling is in Douglas' concurring opinion where he writes:
"The line between what is permissible and not subject to control and what may be made impermissible and subject to regulation is the line between ideas and overt acts.
The example usually given by those who would punish speech is the case of one who falsely shouts fire in a crowded theatre.
This is, however, a classic case where speech is brigaded with action. See Speiser v. Randall, 357 U.S. 513, 536-537 (DOUGLAS, J., concurring). They are indeed inseparable, and a prosecution can be launched for the overt [p457] acts actually caused. Apart from rare instances of that kind, speech is, I think, immune from prosecution. Certainly there is no constitutional line between advocacy of abstract ideas, as in Yates, and advocacy of political action, as in Scales. The quality of advocacy turns on the depth of the conviction, and government has no power to invade that sanctuary of belief and conscience. [n3]"
What he says is that speech and action are inseparable in the case of of yelling "Fire" in a crowded theatre, meaning that such an action is prosecutable.
So in short, you're totally wrong.