Player challenge vs character challenge is a bit of a false dichotomy.
I guess the question is more, "should the character be able to solve problems for the player because of all his or her skills, ability scores and proficiencies?" And, conversely, "should the player be able to override character deficiencies through his or her own intelligence, skill and knowledge?"
The former is a little silly. I don't want characters to be on autopilot. Players have to point their character in the right direction, and the more effectively they can do that (by interacting with the game world created by the DM and other players), the easier things will be for their character. Obviously, players should get a little help from their character skills. I don't expect my players to know how to pilot a ship or disarm a lock. But I do expect my players to know how to listen to what I tell them and ask questions about it.
The latter is, I think, mainly a DM problem, unless players are truly playing in bad faith. (eg, keeping a copy of the Monster Manual under the table, or going home to crib from the adventure, or sneaking a look at the DM's notes while he or she is grabbing another beer from the refrigerator.) Players should be expected to have some degree of meta-knowledge, and while players are always encouraged to play with what their character would and wouldn't know, they shouldn't be expected to completely switch off their own knowledge. That's lazy DM'ing. If the adventure becomes boring because one of the players happens to know stock monsters from the monster manual, the DM hasn't chosen or run the adventure very well. A successful game of D&D should not rely on players willfully ignoring their own good instincts.
Oh, and as for barbarians solving puzzles and what-not, I think we slightly undersell even an 8 intelligence. 8 intelligence is below average, but it's not a drooling vegetable. Furthermore, a negative ability score can be shown in all sorts of different ways. I played a character with 8 intelligence who was capable at talking to people and solving basic puzzles, but he was also incredibly gullible. That was my "this guy is dumb" flaw — he believed everything he read or heard from a person he believed to be an authoritative source. (Decent insight, so not necessarily easy to lie to straight up, but no critical thinking.)