I was at a conference at Caltech. Someone set up boxes of food for lunch. Someone at my table grabbed one and started to eat. I noticed that it said "Stephen Hawking Lunch Gluten Free / Vegan" on it - it was already half-eaten, and I figured it'd be too good an opportunity to pass on, so I decided to eat some of stephen hawking's lunch, literally.
It turns out that despite his physical limitations he actually did eat normal solid foods. This was in 2011.
Hawking's condition worsened steadily throughout his life. While he was wheelchair-bound by the end of the 1960s, he was still capable of speaking until the 1980s. In the 1970s, he was already an accomplished scientist and would probably have been capable of eating a normal lunch.
The timing would even work for the incident to involve the real Richard Feynman. Though, I can't find anything to suggest the story is true.