The recent photos menu does not work for Elements 15. Once you have filled the maximum photos, newer viewed photos do not get added. Elements 14 works as designed. I hope that someone at Adobe is working on a fix.
As an addendum: besides deleting the file "MachinePrefs.psp" also the file "Adobe Photoshop Elements 15 Prefs.psp" should be deleted.
Deleting only the first file does indeed reset the full "recent photo" capability but then a weird effect will happen: the images in the editor window will look strangely "unsharp" unless shown at 100% pixel size (or 50% or 25%). It's like the view in the FastStone ImageViewer without checking the "smoothing" box. After also resetting the "Adobe Photoshop Elements 15 Prefs.psp" file everything will work correctly .... until the next more than 100 opened image files .
I've created a sub-folder "Old prefs" within the PSE15 editor folder containing the actual "prefs" files after a reset. These two files will be copied into the editor folder for resetting purposes.