It seems like we need more context to understand this sentence. My guess is that this is a story about a person who does not believe that anything is an "accident" (maybe he believes that all things happen for a reason? or that when people do things "by accident," it was really because of a subconscious desire?). It's irrational for him to be afraid of "accidentally" spilling food, since he doesn't believe in accidents.
That's my best guess just based on these two sentences, but I could be completely wrong, since I don't know where the passage comes from. It seems like there must be a reason why the writer says "even if there were no such things as accidents," since this isn't a normal worldview. So my guess is that it is the worldview of the character.