Is it even possible to challenge the character? Or does the phrase really mean "challenge the player's ability to build a character, and then use those abilities"?
Thoughts?
While at one level it is true that you can only meaningfully challenge the player since only the player is an active entity capable of making choices, the phrases "challenge the character" and "challenge the player" distinguish between two very different approaches to encounter design.
As an example of "challenge the character", you might imagine a simple locked door. The GM designs this challenge by setting a difficulty of picking the lock, and by setting the difficulty of breaking or bashing down the door. He then treats this encounter as if the ways to get through the door are picking the lock or using brute force to open the door, both of which he intends to resolve purely through a dice roll. This encounter design "challenges the character" in that the player's creativity, skill, and choices don't matter as much as what is on the character sheet. Do you have the requisite skills on your character sheet to pick locks or kick down doors? If you do, then you can gain access to whatever is beyond the door.
By contrast, imagine a door which opens only if a riddle is answered. The GM designs this challenge by making the door immune to any force, magic, lock picking skill, or other devices that the party might have, either by literally writing that as an absolute ruling or by setting the difficulties to overcome the door's defenses so high that he knows the party will not be able to surpass them regardless of how well they roll. The GM then selects invents an actual riddle which he then provides to the players, and he runs the encounter as if nothing on the player's character sheet - not intelligence or knowledge of riddles and enigmas (if there even is such a thing in the rules system) - is applicable to solving the riddle. To solve the riddle, the player must actually answer the riddle. This is an example of challenging the player.
Note that it is very possible to reverse these challenges, making a locked door challenge the player and a riddling door challenge the character, simply by changing the proposition filter that the GM is using during the encounter to determine what a valid proposition is, and by changing the mechanics he uses. For the riddling door, he might actually allow an intelligence check or 'Knowledge (Games & Enigmas)' to resolve the puzzle of the riddle, while not allowing a player to answer without first showing his character could answer. Indeed, in the extreme the GM might simply say "There is a riddle written on the door. Roll Intelligence to know the answer to the riddle.", which means a player proposition like "I say, "Time." is irrelevant because no concrete answer exists to the riddle until the intelligence check is made.
Likewise, it is possible to make opening a locked door a player challenge, by only accepting as valid propositions to open the door the player's description of how their character goes about trying to open the door, such as hammering out the hinges, using a thin strip of wood or knife blade to lift the bar holding the door, or finding the secret catch on the wall to the left of the door and pushing it up, and not validating propositions like "I make a search check" or "I roll open locks".