It shouldn't be breaking any actual links, but by default iTunes will re-organize anything added to it, and that includes compilations where there may be "various artists". How it actually organizes those depends on a few things. I'll explain in more detail in a moment, but the short answer for you is to turn off the option to let iTunes auto-organize anything added to it. Open iTunes, then Preferences, click on Advanced. Uncheck "Keep iTunes Media folder organized" and perhaps even the next option "Copy files to iTunes Media folder" if you want everything stored where you have them already.
To explain further how iTunes organizes what gets added to it, you have to understand the tagging system. Here's an example I have from the Forrest Gump Soundtrack:
On this "Info" sheet for this track, you can see at the bottom that the option "Part of a compilation" is checked. This option forces iTunes to auto-sort anything with that option into a "Compilations" folder in the iTunes Media Library. If not for that option, all the songs would be scattered under folders for the artist of each individual track. Since that's not the folder you are seeing your files under, the next screenshot should explain what you are seeing:
Here on this "Sorting" sheet, you'll see a field for "Artist" and "Sort Artist". This particular track was done by Three Dog Night, but since this album is a compilation of music from various artists, I have the sorting field set as "Various Artists". If this wasn't flagged as a compilation on the other page, then the music would instead have been organized into a folder named "Various Artists". Now, the reason you use Various Artists as a sorting option is to keep the tracks listed together still if you have iTunes open and you click a column to show everything sorted by the artist name. This forces all the tracks of this compilation to stay listed in order of the album and not spread out, something that is reasonable in the case of compilations like this.
Another, and probably more reasonable way of tagging these, would be to leave the "Sort Artist" field blank, but use the "Album Artist" field instead as shown. This way, you can truly sort all your songs in iTunes by artist, but use the album artist if you want to sort an artist's contribution to a compilation like this separately and, for all intents and purposes, treat "Forrest Gump" as an artist. The only downside to this is that you would have to use the "Compilation" option checked to keep the actual files together in one folder.