ASIO is only truly useful for some recording applications, or instances where you want to "sync" one sound device with another---maintaining very low latency.
If your sound card supports bit-perfect output, it is possible to attain it using regular WaveOut or DirectSound output, if your volume dials are set properly. Usually this involves setting Wave and Master volumes to 100%.
Even if your soundcard doesn't support bit-perfect (the majority do not), you can still get audibly-perfect sound with software resamplers. Many cards resample to 48khz internally. So just configure foobar with PPHS resampler to 48khz, and your golden.
And by the way, even though the X-Fi cards DO genuinely support bit-perfect output, it is pointless to use unless you just like placebo effects. I tested it myself---the "noise" the X-Fi's resampling to 48khz added to the signal was in the order of around -130 to -138dB. Nothing you would be capable of hearing, even if you had exceptional hearing, and had the best equipment in the world. With noise at such a low magnitude, in order to be able to hear the low level noise, you would need to turn up the volume to the point where the desired signal(your song) would in fact deafen you. Or if not deafen, severely impair your hearing.
If you have a non-xfi card that resamples(AC97, Live, Audigy), those may actually add noise in the -80 to -100dB domain. This is still extremely low, and will not be audible 99% of the time. If you are after purity, simply resample in foobar via PPHS to 48khz which will push the noise down into the -110 to -130dB range.
Lots of people rant and rave about how they want bit-perfect, but there has not to this day(as far as I know), been one person who could tell the difference between BIT-PERFECT playback @ 44.1khz, and HIGH QUALITY RESAMPLING to 48khz when using their EARS ONLY. (In other words, a blind listening test, or ABX)
Having said that, bit-perfect obviously cannot make the output sound WORSE, so if you already have a card that supports it, you might as well use it. But if you have, say, an Audigy2 ZS(with software resampling to 48khz), and you think getting an X-Fi(or any card with bit-perfect) will somehow make things sound much better, you are pretty much wasting your $$$.
Finally, to get back to your original question which was regarding ASIO--- ASIO does not guarantee bit perfect in any way at all. It simply implies a more direct, low latency path to the soundcard. Once the soundcard receives the data, it is still free to resample or do whatever else it wants, regardless of whether the data came from DirectSound or ASIO. And last but not least, Kernel Streaming has almost the same effect as ASIO (in that it bypasses window's kmixer dll, sending data directly to the card). And just like ASIO, it does not guarantee bit perfect.