How have courts dealt with the issue of whether a defendant has shown evidence of protected speech or petitioning activity?

"At the first step, the moving defendant bears the burden of identifying all allegations of protected activity, and the claims for relief supported by them. When relief is sought based on allegations of both protected and unprotected activity, the unprotected activity is disregarded at this stage. If the court determines that relief is sought based on allegations arising from activity protected by the statute, the second step is reached. There, the burden shifts to the plaintiff to demonstrate that each challenged claim based on protected activity is legally sufficient and factually substantiated. The court, without resolving evidentiary conflicts, must determine whether the plaintiff's showing, if accepted by the trier of fact, would be sufficient to sustain a favorable judgment. If not, the claim is stricken. Allegations of protected activity supporting the stricken claim are eliminated from the complaint, unless they also support a distinct claim on which the plaintiff has shown a probability of prevailing." (Baral v. Schnitt, supra, 1 Cal.5th at p. 396.)

a. Respondent Has Shown that Appellants' Claims Arise From Protected Speech or Petitioning Activity