We use CentOS AND RHEL. On a few mission critical servers running non-FOSS apps certified to run on RHEL, we use RHEL. We want to know that in event of a major problem (especially if I was gone for some reason) we can call the app vendor or RH and be reasonably confident the problem will get fixed. We've never needed to do that, but over the past decade it has remained far cheaper to pay RH than run the same app on Windows servers.
We aren't talking about talking about tens of thousands of dollars to be able to run RH and get updates. If you want the ability to call Red Hat for support on a case-by-case bases, you can get an annual RHEL license for as low as $349 (academic pricing is more like $60/yr!). $799/year gets a 1-hour response for critical issues. But it is up to your boss to decide what level of support, if any, he wants to go with.
For many of our other servers we use CentOS. Some can be down with little affect on the organization. Others are just running basic LAMP and FOSS apps where certification isn't an option or isn't required for support. Frankly there is no benefit to us to use RHEL on these servers as we are able to fully support the OS and recover from even severe problems.
If you don't have any need for Red Hat's services, software/hardware certifications, or anything else that adds value to RHEL, then by all means stick to CentOS. If you are worried RHEL (and therefore CentOS) will go away if you don't support RHEL, insist that your boss buy a contract (and don't complain when you are looking for your new job.)
It is all insurance. As others have said, the real question is how much will downtime cost you? Will RHEL reduce the chance of downtime? Will it shorten the amount of time until recovery? Will it show enough "due diligence" to your boss's bosses to keep both of you employed after a disaster? If you are really worried, fire off a memo to your boss with your concerns and then accept whatever he decides. (But keep a copy as CYA for yourself in case you turn out to be correct.)