Short answer: It's not more important than actual experience. However, if you can't do FizzBuzz, that shows not only a complete lack of ability and a complete lack of preparation, in most cases it shows intentional deceitfulness. I will remind them that there exists a modulo operator and I will explain what it does as I understand that interviews are an inherently stressful process, especially for your first position.

Everyday HTML/CSS has problems that are more difficult than FizzBuzz. It's not a gotcha question, it's mostly there to see if you have actually written any code or if you are submitting a false resume.

Side story: I have witnessed someone with absolutely no coding experience get hired. He not only lasted, he was considered pretty good. His secret: he used Fiverr and some other services to outsource his work. I have to complement the guy. In the end, he completed his tasks and added business value. He wasn't looking for a career, he was just looking for a job that paid well so he could buy a car and move across country. In the end, no one was hurt and both parties got what they wanted.

EDIT: I'm assuming they literally asked about FizzBuzz. It is literally the apocryphal interview question and just beginning filter to see if the rest of the interview is going to be a waste of both of our time. I would assume that if you hadn't come across FizzBuzz that you have never coded before and/or it that you did no preparation for an interview. It isn't all about the difficulty, but FizzBuzz is almost as ubiquitous as "Hello, world."

EDIT Whiteboard Challenge: That said, I loathe whiteboard challenges during interviews. In the past, I've been asked how would I design a Mars Rover and control it from Earth so that it could complete its mission. I didn't know much about AI or computer vision at the time. However, it was for a mid/Senior level full stack position. I had no idea if this were an actual coding question or if he simply wanted to see how I approach problems. I went on about how I would first upload the most precise map data that we have on Mars for the days journey. Then I would make sure the navigational system was accurate by using onboard cameras. The cameras would be looking at certain topological features and how far away they were. If there were a major sand storm that changed the environment, we'd have a problem Houston. I went on about how the Rover would only be given instructions to move as far as can be seen from the original position since the camera feed was not live, but had a delay due to the speed of light. Next, it'd have sensors to know to go into clamshell or whatever mode if it detects a major sandstorm to protect the fragile instruments onboard. He still said he wanted more, so I totally bullshitted something about whether Mars was in its perihelion or not, I'd make sure the Rover only moved during the day etc.

After about 15 minutes of this, he said he was looking for the Rover to be implemented as a RESTful API and Houston would represent the client. I looked at him quizzically, said that was the worst interview question I've ever heard, and I think we're done here. When I got home, I did some googling and found that he ripped this as an interview question: http://stackoverflow.com/questions/185740/would-you-architec...

Now, I know that Microsoft Robotics Studio uses REST and, although I am well past whiteboard challenges, if anyone asks me to do one, I will politely tell them that its unrealistic and never the way I would first approach a problem since I never write code freehand. I frequently draw diagrams, concepts, actions, etc. on a whiteboard. I would be more than happy to actually sit down in front of a terminal, load up an editor and write code that I can get an actual output from. If you can't, then, from my perspective, you're basically asking me to code with one tied behind my back while blindfolded. If that's what you want, I hope you find it, but I am not the right fit.