Both ways of looking at it have their advantages and disadvantages. I wouldn't advocate making every SC work only with the skills the party happens to have, but I would advocate trying to design SCs in such a way that its unlikely a typical skill distribution of a party will leave some PCs unable to contribute. I think that's more the issue with tailoring SC than making them easy for a given party.
I'll draw the analogy to the debate in the thread on flying creatures. A good DM will probably not suddenly have a dragon show up and ravage the party from the safety of the air at 20+ squares range without given the party some alternatives. Even though you could say "Well, they should have invested in X,Y, and Z for that eventuality" its unlikely that every party will have contingencies for every single kind of situation. Likewise with SCs. Challenges will come up that nobody anticipated or it was just too expensive to plan for.
Now, that doesn't mean the DM should axe the dragon idea, he should just make it more interesting than "the party runs in fear from the undefeatable enemy". He doesn't have to let them win, but defeat can be made interesting. "The party flees into the woods where they run into the refugees of the village the dragon burned." Likewise with some kind of SC the party can't handle. In other words you might call it tailoring the SC, but its more like just making sure the narrative accounts for every possibility.
The real tailoring issue with SC then is "the useless character". For example I have an SC I designed last week for my group which I haven't run yet, but it basically consists of climbing down a shaft to a tomb while ghostly spirits try to frighten the characters away. It could have been just a climb, but then how do the wizard and the starlock participate since they mostly have knowledge skills. That's where the spirits come in. It adds a dimension to the challenge that they can deal with by using some history, religion, and arcana checks as secondary skills to erase a failure, give a bonus, and unlock another primary skill. I'm not sure I would say this SC is "tuned to the specific party", but it has a balanced set of ways that knowledge, social, and physical skill sets can contribute. That would probably make it a decent challenge for most parties.
Of course unfortunately WotC module authors don't always seem to be the best adventure designers so if you run prefabs you will often find one-dimensional encounters (both SC and combat). I guess either you have to tweak them or just not spend money on modules. Personally I haven't run a module in probably 10 years at least, but then I'm crazy that way...