I've confirmed that with the default tolerance of 0.1 the magic "width" where the behavior changes from drawing a bevel to a round line cap for a right angle join is 0.6828. There is also a bug in the Cairo code where a tolerance larger than the stroke width can result in round line caps (there is a squaring of a negative number in the calculation which leads to an invalid result).
I've confirmed that with the default tolerance of 0.1 the magic "width" where the behavior changes from drawing a bevel to a round line cap for a right angle join is 0.6828. There is also a bug in the Cairo code where a tolerance larger than the stroke width can result in round line caps (there is a squaring of a negative number in the calculation which leads to an invalid result).