The important thing to plan for when using 3rd party controls is continuity. If they do go under, what does that mean to you? How much are you relying on their framework, and how much work would it be to switch to something else? IS there something else that does what you need?
If you have source code for the component in question, it puts you in a much better position - you can at least fix bugs and possibly even maintain/extend it yourself. On the other end of the spectrum is tightly controlled software, where you have to renew every year and it expires if you don't. If you're using something like this, if they go under, it forces your hand, and you'll have to do something.
It's really a balancing act. Saving you work/money vs Probability of them disappearing vs Relying on a 3rd party.
I once had a boss that was like yours. The thing they miss is that you're entirely relying on 3rd party. If you're using .NET, you're trusting that Microsoft is not going to go under (probably not..), discontinue it (maybe), or radically change it (quite possible). Of course he's gone now, and we've since started using a handful of 3rd party controls (some open source) that have saved us hundreds of hours of dev time, or just let us do features we never would have done otherwise (because it would take too long).