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A frictionless mechanism is me after a few pints of Guinness and a hot curry! 
I like undersea tunnels' Eurotunnel is the best way of getting to the mainland with your car but its so dammed expensive.
I believe I've heard the same thing and that the figure of ~42 minutes for any two locations is correct. This all depends upon a purely gravitationally effected journey though - the longest journey, through the center of the Earth, gets the greatest acceleration whereas a shorter journey, which will be a chord, gets a proportionally lower acceleration, accounting for the similar journey times. I've got an idea it may depend upon the Earth being homogeneous though, which it isn't.