I can't believe that this thread is still going on. Isn't it obvious that the DM can determine different results based on the individual characteristics of the PCs? Consider two examples:
1. The PCs are trying to remember the name and other facts about a drow queen 500 years ago who founded an enormous temple to Lolth in an underdark city. PC A is a human wizard that is proficient in History, but has lived his entire life on the surface and (ala Greyhawk) had never heard of drow before this adventure. PC B is a drow cleric that is proficient in Religion, but not History, and was actually alive and living in the city at the time the temple was founded! The adventure calls for an Intelligence (History) check. PC B actually rolls higher than PC A, but because PC A has a higher Intelligence and is proficient in History, PC A's adjusted result is higher than PC B's adjusted result. What reasonable DM is going to say that PC A knows more about the drow queen than PC B?
2. The PCs are trying to rapidly wade a swift mountain stream that is four feet deep without being swept away. The DM decides to call for a Strength(Athletics) roll. PC A is a halfling is small for his race, merely 2 feet, 8 inches tall and weighing only 35 pounds. PC B is a larger-than-average dragonborn, at 8 feet tall and 350 pounds. PC C is average size, but is an sea elf who specializes in water element spells. Is the DM really going to say that for purposes of determining success, the only relevant factors are the PC's strength and proficiency bonus?
Personally, I would not express the differences among the PCs in the above scenarios as different DCs; instead I would express the difference as differential bonuses to the PCs (that dragonborn gets a +2 bonus on the check, while the halfling has a -8 penalty). To me, the DC is the "objective" part of the success/failure criteria, and the "subjective" part is each PCs individual bonus. But if another DM would prefer to describe the halfling as needing a DC 20 check to succeed, and the dragonborn as merely a DC 10 check, I'm perfectly happy to go along.