For the most part, Tyson's rather relaxed in his practice of Judaism, but it is still very important to him. He may only make the effort to eat Kosher on Saturdays, but he makes sure to each Kosher on every Saturday. Sharing meals is an important part of Jewish culture, even more so 'breaking bread', specially Challah.
If Tyson is willing to share bread - not a sandwich, but specially a loaf or roll of bread - with you, you are very important to him. Even if the bread he offers you isn't Challah, the symbolism is still there to Tyson. He's unlikely to explain how important sharing bread is to him, unless directly asked, because - for the most part - Tyson keeps his religion private.
If Tyson is willing to share actually Challah with you on the Sabbath, you are something Tyson is willing to die for.
If someone rejects Tyson's offer of bread, he's unlikely to take offense; being someone who views eating a chore generally, he understands not wanting to take the food. The exceptions to this are people Tyson knows to be Jewish - as he'd expect them to understand the symbolism - and people who he's explained the meaning to. Even if the bread isn't eaten, Tyson prefers that the person accepts the bread from him.