As with all things, "it depends..."
Does a dvd replace a qualified instructor? NO
Can a person who has good visual skills and a kinesthetic learning style be able to self-teach to some degree and be proficient? YES
Now, here is where the grey areas come into play. You can have a great instructor and a not so great student, and the student will only see what he wants to see and never make the corrections that the instructor gives. You can also have an average instructor with a very gifted student that can learn and make the necessary adjustments through feedback with their partners and be very good.
For example, former UFC Champion Evan Tanner (rip) learned his submission grappling skills from a video set and some training partners. Lots of hands on and trial and error. Which brings to the next point, the journey is MUCH faster with a good instructor to help point out "pitfalls" in your training so you don't lose time.
With a "live" instructor or a dvd, you HAVE TO HAVE a training partner to get feedback. The training partner, no matter what route you take is one of the most important parts (the MOST important part if you are learning by dvd) to actually attack properly and realistically to learn how to make your technique work.
The reason I have this view is, once upon a time ALL martial arts were self-taught and then refined. So, if you are just talking about "fighting skills" then that is one thing. BUT, if you are trying to pass down a traditional system and to teach it the way it is supposed to be taught then you have to learn from an instructor in that style. Even styles that are "close" in mechanics you will have the external shell of the forms and basics but may not have the internal "tweaks" that the style uses that sets it apart.