You know, I thought Hawking was smarter than this

1) I think the most obvious thing is it doesn't disprove anything, what if time travelers just didn't want to show up or never saw the invitation? If I could time travel, I wouldn't want people knowing about it

2) He already knew the result of the experiment before making the invitation, thus making the act of making the invitation is pointless.
3) The other possibility is working along the principle of the multiverses; Stephen Hawking #1 would have the party, make the invitation then a time traveler would see the invitation and travel back in time, travelling in time creates an alternative universe where he would meet Stephen Hawking #2. Thus Stephen Hawking #1 never meets the time traveler even though he's the one that set it in motion. Hawking #2 can then not even bother making the invitation but the act of making it could make more time travel possible for Hawking #2+n and shiz starts getting complicated
