My mother recently started having to deal directly with utility bills and the like and this was some information we impressed very early on. You should never agree to billing or hand over CC/account information in a phone call you didn't initiate. She hasn't run into an issue yet - most utilities, online stores and other entities have call in numbers if you need to resolve a billing dispute. That random company you bought a plumbing valve from has an office somewhere with a secretary that gets a phone call maybe three times a month from customers looking to resolve issues - and Amazon has mostly centralized support for small sellers and has lines you can call to resolve any disputes you have which may forward you to the original sale party but often just resolve the issue directly.

Honestly, the worst experiences are usually with large companies that funnel all customers into massive phone centers - I've probably lost the better part of a week to Comcast over my lifetime.