Following a design brief...is it really important?

What is really important is that the clients needs are truly met and depending on who wrote the design brief it could (or could not) be an important element during the design process.

Illustrated here

If you don’t follow the design brief, all you’ve done is created a pretty picture. You are always welcome to create an alternative concept, providing that you can do what was asked of you and the alternative within the time budgeted for design. Make sure you draft a design rationale for the additional concepts, and append the design brief. If the alternatives look too finished, the client may question the billing. I always had the designer show me pencil roughs of their concepts, and then I would make the determination if we wanted to invest in more copy time on a secondary concept. Depending on the client, sometime they did. But, we could never bill for it if the job was already at estimate. I’d have to make up the cost in increments on future billing.

I agree with drClaw it is important to know what they client wants and you should check if your work meets their requirements, communicate with them as much as you can

I don’t know how you can design without keeping all of that info in mind. If you are designing for someone, then you need to know what they want, and you must do all of your designing to meet the expectations and needs of the client. It is rather like a recipe for a fancy bread! You follow the ingredient list, but you may add or modify them to improve the finished project. But it still needs to end up being a fancy bread that meets specific tastes.

Isn’t a design brief a sort of specification for what the client wants? If I specified ‘a’ and the designer delivered “AAA”, then I might change my mind and accept that—if the price wasn’t too high, and if it at least suited my minimum requirements for ‘a’. But if the designer delivered ‘BBB’, then I may not even listen to the sales pitch, and just toss them out of the office as non-responsive.