Note that a good part of what gets captured with 24-bit recording is the ends of reverb tails and room sound. You can often hear that stuff into the noise floor, especially if you raise the level way up.
Now, many if not most sample libraries are either normalized or raised so they're playable. And there's also a good chance you're going to compress them, which will raise the low-level details (even if your goal is to smooth out the sound and increase the density).
In that case it almost certainly doesn't matter whether you use 16- or 24-bit samples. That was Andrew K's conclusion when he released LASS, for instance. He included 24-bit programs as well as the 16-bit ones, but the first release was a few years ago when memory and storage were both scarce resources.
Yes, if you've recorded at 24-bit, and then done some normalizing / level changing to bring up the samples to a healthy level before playing them in a sampler, then it's much more acceptable to use a version of the samples that have been truncated to 16-bit.
I often prefer to jack up the level of softer samples, and then use the sampler's velocity>volume functions to recreate the dynamic scale - this allows me to lessen that effect, which "compresses" the dynamic range. This sounds different to applying an audio compressor plugin on the sampler's output, and is more of a "playing" effect rather than a "mixing" effect.
So in those situations, as with LASS, storing and playing the samples in 16-bit format isn't a high crime or misdemeanor - but when it comes to the original recording process, doing it at 16-bit means you've got to be very careful about recording levels to avoid accidentally capturing only 9 bits worth of signal on the softer sounds. That's why I'm sure LASS was recorded at 24-bit, then edited (and possibly normalized / gain changed), and then output in both 16 and 24 bit formats. This makes sense.
But many sample libraries do not raise the gain of softer samples - they may "normalize as a group" but not get into the weeds with trying to normalize every sample. One reason why the developer would do this is because it's easier to accurately replicate the original playing dynamics of the original instrument, by insuring that the sampler's velocity>volume amount is set to zero (which is sadly not always the case). Then a soft sample plays with the same gain applied as the loud samples, and everything should play back as it was recorded. Although this approach is the easiest way to replicate the original dynamics of the samples as they were recorded, it can make it difficult to do the "compress dynamics" thing I described above - in order to do so you'd need to apply an inverse (negative) amount of velocity>volume, so that the softer samples get played back louder than they were recorded while the louder samples get played back normally (basically). It's this type of library where the 24-bit-ness of the source samples is more important - if they're stored at 16-bit then those soft samples will be at an unacceptably reduced bit depth and will possibly then be boosted in level when you muck about with the velocity>volume amounts, perhaps revealing their truncated depth even more.
If we're talking about a drum library where velocity usually controls volume, this analogy holds mostly true - but when we're talking about a string, brass, or winds library where you're crossfading between the quiet and loud samples from the mod wheel or whatever, then it becomes even more likely that a quiet sample will be played loud - and if you're in 16-bit mode then it's even more likely that you'll reveal a truncated / low-depth sample.
In this age of cheaper memory and storage, and fast SSDs, just staying at 24-bits all the time is not as much of a performance penalty as it was when LASS was released, when a 500gb spinning drive was state-of-the-art.
TL;DR part 2 = Always record and edit audio at 24-bit (unless maybe it's a low-dynamic-range source like metal guitar or something like that where 16-bit might be more acceptable... but still). Don't fear using 16-bit versions of sample libraries if they're provided, especially if the samples within the libraries have been normalized - but keep an eye/ear out for any situations where quiet 16-bit samples get played loudly.