Legal Question in Civil Litigation in California

Proofs of service don't require exhibits. They're just sworn declarations about when and how the signatory served the documents. But remember that service is not the same thing as delivery. Some deliveries would qualify as service, but most would not. It's not enough to show that the defendant has seen the papers. You have to show that the way the papers reached him met the requirements for service of process.

I don't know exactly what the insurance company's letter says, but it seems to acknowledge only that the summons and complaint were delivered to its offices, not that they were served on the defendant. That's a long way from what you would need to prove. After all, the insurer is not the defendant.

You say "Plaintiff served defendant." Ordinarily the plaintiff can't do that himself. So if you delivered the document on your own, the defendant probably was not served. Even if you mean that somebody else did it for you, it's still very possible that she merely delivered the documents but did not perform a valid service. If she did it correctly, she can sign off on a proof of service without attaching any further evidence.