If the doctor had an invite then surely he would of made it and seen his future self get killed, why would he only turn up to the diner. I think the 6th person on the beach is the younger version, any other thoughts?

I'm sure The Doctor said he was given a time and place - that time and place doesn't have to be the same as River's & Amy/Rory's.

CED3's time and place was different to theirs as well.

Amy, Rory, River = At the roadside
CED3 = Slightly later at the lake
The (younger) Doctor = slightly later still at the Diner

He seemed rather oblivious as to why they were there though, why?