It looks like insured one can't speculate about extraneous 'facts' to trigger Duty to Defend:
An insured may not trigger the duty to defend by speculating about extraneous ‘facts’ regarding potential liability or ways in which the third party claimant might amend its complaint at some future date (Gunderson v. Fire Ins. Exchange (1995) 37 Cal.App.4th 1106, 1114.)
But can insurer speculate about extraneous 'facts' to avoid Duty to Defend?
As a hypothetical example, imagine scenario where commercial general liability insurance policy holder is sued by a third party claimant for property damages as defined on California CIV-050 "Statement of Damages (Personal Injury or Wrongful Death)" form that was served to him along with complaint. But throughout complaint the plaintiff/claimant fails to mention how exactly he incurred property damages to any of his tangible property.
Would insurer be allowed to "speculate" that claimant with property damage most likely meant something else than defined in policy? And put burden of proof on insured to prove otherwise before duty to defend is triggered?