Of all the searches I have done, I can't think of a company whose board of directors didn't instruct me to investigate the current CEO first.

It means:

I didn't expect that any research I did was introduced by a board of directors to meet the current CEO first.

Sentence analysis:

The board didn't instruct me to consider the current CEO first.

This is an adverbial clause, in which is a leading word, which is similar to the Chinese word "among them" and cannot be replaced by that. Because it can't reflect the artistic conception of "among them"

Here, this clause can also be regarded as modifying the search.