There is vertical compliance to keep the tip in the groove and handle record warps. Just higher compliance laterally. No vertical compliance means the stylus bounces in the groove from record warps.
yes... and interestingly enough the choice of the day was to use a rectangular cantilever cross section with a high aspect ratio to put all of the rigidity in the lateral direction. The flex of the cantilever in the vertical direction is what dictates the compliance and as you mention, it is a much lower value than the lateral number.
dave