That's true of most companies, unless you're a customer or they think they can sell you something, they're unlikely to give you much time even if you can theoretically call them up.

In this case, you point to the hypocrisy of being uncontactable but demanding your contact details, except that Google does provide support to customers, and in this relationship they are essentially a customer of your CT log, and given the criticality of that service they rightly expect the service provider to be held to a high standard. I don't think they're holding you to a standard that they themselves wouldn't agree to be held to for a service that critical. I've got to make it clear that this is my personal opinion though.