Here's my take on "try not to say no" in the context of skill challenges:
There's a well-established approach to RPGing, in which the GM has a conception of the fictional situation that they have only partly shared with the players. When the players ask a question (say, "Is there a market stall at the foot of the wall?") or declare an action, the GM answers and adjudicates by reference to that conception. My experience is that this produces an approach to play where the players declare actions that are "low stakes" in terms of risk, but are likely to prompt the GM to tell them more, so that they can enrich their conception of the situation to bring it more into line with the GM's.
A classic dungeon exemplifies the preceding paragraph, but is by no means the only sort of fiction and situation-design that does so. Things like "This guard is too upright to be bribed", "This king is too important to give the PCs an audience", "This cavern is too wide to be jumped", "There is no sustenance to be found in this desert" - all as decisions made by the GM that generate adjudication of declared actions - are examples of a sort that I often see discussed.
"Try not to say no" is an injunction not to use the approach just described. The situation is what has been presented, not other stuff the GM is imagining. "Is there are market stall?" - either say 'yes', or else call for a Streetwise check (do you know where the market stalls are?).
The 4e DMG2 spells this out a bit more (p 16): "player suggestions must remain consistent with the world's previously established continuity. . . . This stipulation only applies to facts about the world that have come up in play. You can contradict a detail about your setting that, so far, appears only in your notes."
This "try not to say no" approach reduces the "puzzle-solving" element of play. My view is that it tends to increase the "vibrant shared fiction" element. This is what skill challenges are for: to create vibrant fiction with reasonably clear stakes and consequences that flow from those stakes.