> Understanding of trees that I don't have to implement.

The main purpose of understanding 'of trees' is not to re-implement them (I have done that though) but in order to know how to use use them effectively. This is about knowing how your tools work. If it is hammer, well, it is hammer, but some of these tools are pretty complex and it is worth spending time understanding what trade-offs different data structures have.

You don't have to get a 4 year degree by any means to do that you can also learn that on your own.

> I ended up managing the one with the PhD, not that it matters.

So if it doesn't then why are you mentioning it. Maybe maturity and the ability to communicate should be #4 in the list?