It's not a watermark. Well, probably not in the sense you're thinking of, anyway. But, I do know what's happened. When you've saved your 'silence' you've started with a 16-bit int file, and the artifacts you've got are the sounds of lsb noise with an mp3 coding gain - you can tell this simply by the level they're occurring at, which is about -96dB (the 16-bit noise floor).
The reason that the noise is somewhat 'discrete' is that to code an mp3, the audio is split into 'critical' bands, and an evaluation is made as to where the inaudible bits are, and these are coded at a reduced bit depth (the masking process). On top of that, when it's silence, it's all about the lsb, and, especially if a file is dithered before saving, there's random noise at that level. Since a transform is done, you end up with a statistical removal, and this is the sound of the result. It's pretty much the same as overdoing NR - that results in a very similar noise. To sum it up, what you've got is, at its heart, coded dither!
Just to prove this to you, have another go. This time create a 32-bit file of silence (which is inherently not dithered), and convert that to an mp3. I have tested this, and I saved mine at 320k, although this should make no difference. Anyway, try it and see what you get then... 