This is why you need a balanced view. These Stats people do have information to contribute to the conversation, but they aren't, nor should they be the entire conversation. It's the same as the old school people, and the eye test... they have thoughts and opinions that should be part of the conversation as well. It's when you can properly take both stats, and old school smarts, to make they useful that you have the right read. Both groups can learn off of each other.
I think it is also very important to note that "stats" people, at least legitimate and reputable ones, are not just looking at spreadsheets and numbers. There is a lot of logical inferencing and application, much of which is the same sort of mechanism used in the more subjective methods of evaluation (i.e. eye-tests), required to properly use statistics.
If anyone knows anything about statistics, that is pretty much the first thing they teach you about statistics besides basic probability.
Otherwise, you'd get a bunch of people saying Sandin-Dermott is better than Rielly-Brodie because they have a higher GF%... totally ignoring the fact that Rielly-Brodie are playing far tougher minutes with more defensive responsibilities, and therefore would need to be absolutely exceptional to do as well as guys in a lesser role.
One of the many things statistics can do is create an intelligent and objective guide to subjective methods, and the way I look at it, is that they effectively act like another scout, evaluator, coach, etc. when used in the right hands.
For example, Scout A, B, and C can all say similar or completely different things about Player X, and those may differ completely from what statistics will say about Player X. You can't entirely trust statistics because, at this point, they don't cover everything about a player. At the same time, you can't just trust Scout A, B, C because they each have a subjective perception of the player. Even if they are experts in their fields, they are still prone to make a lot more mistakes than objective means such as statistics.
And that is why, as you said, you use both. If you don't, you are asking to be left behind.
