The trouble with a solid white background is that if the image you want to lift out has shiny parts, metal parts, lens flares or anything of that nature, Photoshop (and Elements) will have trouble cutting out the background without taking out parts of the image with it, as you saw. This will be true of any of the broad attack tools like the Magic Wand or the Magnetic Lasso.

Reducing the tolerance will certainly reduce the amount of the image that you lose with a tool like Magic Wand but it will also leave more and more of the background around the edges of the image--that's what causes the ugly white border you see around graphics on some websites that kind of make the picture look as if it was stroked in white. If you do manage to get Magic Wand to select only the parts of the image that you want, you will notice that the edges of you newly lifted image are ragged, ugly, and not of adequate display quality. Now you have no choice but to attempt to trim, clone, smooth, and smudge each edge and side of your image where you removed material. This is very time consuming and can be very, very frustrating. Also, it's nearly impossible to this make type of work look professional.

If you aren't skilled with making a mask for your image you will be much better served if you take the time to create a clipping path and save the image with the path intact. Even the most complex images won't take more than 30 minutes to path out precisely and you have the advantage of being able to save your progress at any point and pick up where you left off later. Once you have completed your path, convert it to a selection and cut it out. Now you have a lovely, perfectly smooth lifted image for whatever you needed it for!