Can you "know" a character if you're not in his/her head?

Quick answer: yes, you can.

Most often, though, I see this question in internet writing discussions, and it's not framed as a question. I see people saying, "I think I need this point of view in my story so people will be able to know the character better."

No, you don't necessarily.

I like to think of it this way: we don't "get into the heads" of people we know in real life, yet we do feel we know them. The way we get to know them is by observing their actions, listening to their words, and drawing conclusions about what they are thinking. Babies typically learn to construe others' emotions on the basis of facial expressions at age 9 months, and this changes everything about the way they interact with others. What I mean by this is that as humans we have a very strong basic instinct to read emotion from facial expressions - and this extends to construing motives etc. on the basis of others' behavior.

As authors, we can take advantage of this instinct. Non-POV characters, treated properly, will reveal their own thoughts and motives. The key, however, is that the author must know the auxiliary character's thoughts and motives. Thus in order to make it possible to write characters without having readers need to be in their heads, the author must be taking a look into their heads.

I can't tell you the number of times that I've written a scene and felt it wasn't really coming across quite right - but when I went back and looked over it, I discovered the problem was that I really didn't understand the emotional state and motives of an important secondary character. Sometimes a non-POV character can be so minor that his/her emotional states aren't particularly relevant (like a guard who takes no action, for example). However, I urge you not to underestimate how often people construe others' motives without even realizing they're doing it. It's always my habit to have point of view characters move through their world judging people and events, and thus I will occasionally find opportunities for characters to toss off a guess at what a minor standby character is thinking. By doing something like this, you can accomplish two things: first, you can say something about the main character's state of mind (like having him be self-conscious and wondering what others think of him), and second, you can imply that any character is potentially worthy of having his/her motives guessed at. This can encourage your readers to guess at the motives of minor characters more often, and give your entire world a greater sense of depth and dimension.

So when is it a good idea to make a character into a point-of-view character? I'd say that it's a good idea to use a character's point of view 1. when that character "owns" a vital piece of the main conflict and 2. when knowledge of that character's mental states enhances the main conflict rather than detracting from it. This previous post, Multiple POV or not?, considers some of the issues of including or excluding a character's point of view. Basic summary: just because a character has opinions, or even an important role, doesn't mean that you should include his/her point of view. My point here, however, is that it may be very important to understand what the character's point of view would be like.

What I suggest, in a case where you really want to know a secondary character deeply, is to write a piece from that person's point of view. This can be a part of the work-in-progress, but generally when I've done it I've done a completely separate piece, almost a short vignette story, having to do with some backstory event that helps form that character's personality and motives. I initially wrote my Panverse Eight Against Reality piece, "The Eminence's Match," as a piece of backstory for a major non-POV character in the trilogy I was writing at the time. I can't tell you how valuable that experience was for me, or how inspiring. I then was able to go further back in time, and get further insight, when I started writing my current novel. The more complex a character is, the more valuable it can be to know them deeply. That way their words and actions will make ten times better sense, and come across as real to readers, even when they are acting without the support of internal point of view.

It's something to think about.