This is the BOTTOM of the board. He doesn't want a piece of string hanging from it when using it. The string gets threaded in when the handle is used.
(Why not put the handle string on the top of the board permanently?)
Ha. As I was reading this I was thinking "glue on padeye etc" till I got to your last paragraph.
Your idea sounds reasonable if the top laminate has any thickness to it. Usually foam boards are made of pretty light foam with almost no strength so you can't rely on the foam doing much.