That’s right, @Brent_Ross. Tasks assigned to you are by default put into the New Tasks section of My Tasks. More info on how My Tasks is set up here. As you can see in the posts above, I like to add section headers to my Today section in order to organize my personal tasks. Since you want to use My Tasks as a dumping ground, you could create sections under Today to help you organize that dumping ground for GTD.
For example, if you want categories to reflect the five pillars of GTD, you could use New Tasks as the “capture” step and then under Today create sections for clarify, organize, reflect, engage. This is just one idea of many. I think you might enjoy asking for input from the group in this Community thread about GTD.