Yes. That is the classic argument for that interpretation. And it is absolutely a valid argument. There just are other interpretations with similarly valid arguments associated with them(Granted, there could be some abilities that has a form that makes the ability hardly worthwhile if everyone could do it via some other mechanism - but I associate that more with PF than 4ed)
If by "interpretation" you mean, doing what the text of the rules said to do, I agree. The other argument I see is that you don't use the rules provided. There is text about using skills the DM hadn't considered or other benefits not connected to the skill challenge and, of course, not everything is a skill challenge. But for the challenge itself? It was X successes before Y failures and every character must contribute. I'm sure some tables did alternatives, I know I did after a while. I don't remember is the later DMGs or Essentials changed things or not, it's been too long.
From the 4e DMG, I just don't see any wiggle room.
The Basics
To deal with a skill challenge, the player characters make skill checks to accumulate a number of successful skill uses before they rack up too many failures and end the encounter.
Example: The PCs seek a temple in dense jungle.
Achieving six successes means they find their way. Accruing three failures before achieving the successes, however, indicates that they get themselves hopelessly lost in the wilderness.