If the software is copyrighted, you can't make a derivative work without permission, and that's what modifying it is doing. It seems silly to say that a modified program you use only on your own computer is any more a "derivative work" than clipping photos out of newspapers is, but the EULA typically specifies conditions you must agree to in order to use the software, and you don't really get a say. All the rights are with the creator.
This is not correct. The copyright only restricts distribution. As in, you are not allowed to distribute a derivative work without permission. You certainly are allowed to create derivative works for your own usage. Also, clipping photos out of a newspaper is not creating a derivative work anyway, it depends what you do with them. I suppose if you clip a photo, trace some outlines and colour it in with crayon.. that would be a derivative work, depending on how closely it resembles the original. If significantly different it might be considered a new work.