No, you're quite right. Many are assuming that all you have is collagen, but it sounds like you also have fat in your stock.
Tricks for removal include the ones mentioned (ice, fine strainers, etc.). Also:
Bring very briefly to a boil, add 1/2 cup cold water, stir, shut off heat, let cool to room temp., refrigerate. This can help break a partial emulsion and release fat. It's easy, but it doesn't work well.
Clarify, as with consomme. Put a bunch of very lean meat (e.g. skinless breast meat), preferably ground, together with some finely chopped vegetable mixture (same group you used in making the stock), and the cold stock in a pot. Add a bunch of beaten (but not at all whipped) egg whites; you can add the crushed shells to the meat/veg mix if you like. Bring slowly to a near-boil, stirring constantly. As soon as it reaches a near-boil, stop stirring at once, reduce heat as low as you possibly can (you should have to look very hard around the edges to see any evidence of motion below the surface), and wait about 1 hour. Shut off heat. Tilt the pot gently and very gently ladle off the clear stock, being careful not to break the "raft" of stuff that is floating on the top. (Julia Child has a lovely explanation of how to do this in Mastering The Art.)
If in the end all you've got is a few little droplets floating on the surface of otherwise clear stock, cheat: lay a piece of paper towel on the surface and remove immediately. It will absorb the little floaty bits (and a little bit of your stock, of course).