I.e. that the director is a good advocate and protects the MD/PhD students when either the med or grad school starts being unreasonable.
How important is it to have a "friendly" director?
To be honest, it's hard to gauge this from where I sit. You have to keep in mind that the #1 priority for an MD/PhD program director is to strengthen and grow their MD/PhD program with a minimum of problems. You will find out that all big name PIs and successful administrators are excellent politicans. A smile, an interest in you, a personal apperance... These are all necessary to be the big cheese. I'm not saying that these people fake their outgoingness for their position--they were probably decent people to begin with who have a genuine interest in career development.
You can hunker down and be a total ***hole in your own lab and bring in the funding, but to run an MD/PhD program you have to negotiate with an MD program, a PhD program, students, and a multitude of PIs. It seems to be a relatively thankless job that helps detract from your own goals of supporting your research enterprise and whatever outside hobbies you have. So my point is, all directors are going to be friendly and generally well-viewed. Only the senior students are going to have a real viewpoint on how they feel about their own program's director, as junior students are not in a position to truely evaluate what's going on or to have been in trouble they needed to be bailed out of.
That being said, the director also has to be a politican from other standpoints. The MD/PhD program has limited capital they can throw around to get the MD/PhD students what they want. Some directors highly go to bat in this regard, and others will tell you to deal with bad things because they're trying to reserve what power they have for when they really need it. Will your issue go ignored? Possibly. Is this a good idea for the good of the program? Possibly. Is your happiness the #1 thing for the growth and success of a program? It's a crucial factor, because nobody wants to see you drop out or kill yoruself, but it also has to be weighed in with the willingness of the NIH and the medical school to fund the program. This is politics at its finest and most necessary. Everyone sees things in different ways and there isn't necessarily a bad guy.
So this is a long answer to say: it's complicated. There's no straightforward answer to this question. But, in general, all directors should probably be viewed as friendly and on the student's side unless you get some sense otherwise. At my own program I have heard many viewpoints about how the current director is viewed vis-a-vis the previous director. Everyone sees this differently. One thing that has definitely changed is there's more control and more rules in the current program in an attempt to streamline the program and cut back on problems that come from bad experiences in the past or from people taking advantage of laxity in the rules. Many senior students and some PIs feel this flexibility is a negative, as in personal situations sometimes this flexibility would help in various situations. But you can obviously see the appeal from running a large program smoothly and trying to protect your own students from bad things.
Personally, I gleaned a lot about programs from interviewing at them. Did they seem disorganized on interview day? Did the MD/PhD office not respond to your queries or take forever to do so? Were other strange things happening? These are all signals of things to come if you're a current student there. On second look everyone is going to be on their tippy-toes and cheerful in a recruitment effort, but think back a bit and you might see some things that are concerning. I mean don't blame your interviewers for goofiness, unless you had a lot of them or something, but think about the MD/PhD staff/faculty/directors and think about how they seemed BEFORE you got that acceptance. Some schools do a better job of putting on the dog and pony show than others, but I still think I learned a lot from just that.
Any advice or signs to look for to see if it is indeed the case or it is just smoke and mirror?
I've never seen any student openly despise their MD/PhD program's director. If too many did, the director wouldn't be director for long. Ask the senior students how they feel about the administration. The honest ones will give you the same kind of mixed response I did. I doubt you'll find much hate and you'll likely find much love depending on who you ask. In the end, I'd consider this a very minor part of selecting a program.