The timing is pretty intriguing, since intentionally copying code and ideas that rapidly would actually be an impressive skill of its own. You are left with something that certainly would feel like mind reading.
Sometimes you see this sort of thing happen in movies. My personal belief is that at some point there was something unique happening on a grand level that triggered thoughts of a specific problem and its solution in both of you, yet subtle enough you might never backtrack and discover that commonality.
I hope that you both can move forward without the usual red tape that this would create if you were both megacorps. It's awesome that you both kept it civil and even had nice feedback for each other.
And remember, great minds think alike.
