You're absolutely right in what you say Longshadow. I hadn't thought of it quite in that light!

Does that mean, though, that one should dump the whole possibility of detecting alignment? And if so, the whole alignment system?

As a player I've never really valued the whole concept. And as a DM it can lead to problems if you move beyond there being moral absolutes of good and evil and no shades of grey in between.

I may not exactly be "right", but it is a modified version of how I used to look at the whole Detect Alignment thing.
Olan helped clear things up for me, too.

Dump the system? Absolutely not! It is a useful tool, and was devised with forethought to playability and balance. But the DM has to step in and take all the aforementioned information into consideration when the character attempts to detect alignment. Then, if it fails, she (or he, for all you equal-opportunists) has to stand by her guns and NOT give the reason for failure to the player(s). The best way for the players to realize why it failed, if it failed, would be hints to lead them to that realization by deduction on their part. These hints could take the form of actions or occurrences. For me, that is what role-playing is all about.
(edited)
Oh, and one more point (thanks Utan). "Detected evil" isn't always a bad thing. the subjective thing again. An evil person casting Detect Good would see any detected good as a bad thing and would simply not detect any evil (which would have been a good thing) ...

That whole session just drained my brain. Can I just go sit in a corner, drool, and pluck my lower lip for a while?

*nods* But only if you promise not to drool on the carpet.