Why are you assuming that stiffer=more grip?
You've only as much 'grip' as the tyre can supply for the appropriate vertical loading (eg.weight transfer), it is how the chassis reacts to that lateral force from the tyre.
A softer chassis will decrease contact patch load variation slightly, this would work the other way as well (as per 'Bigjim' suggests), in that driver input does not affect the tyre contact load as rapidly, or to the same degree.
It's all relative though, depending on the stiffness in the first place. Some people need to run extremely stiff in the wet, others very soft. I wouldn't get too hung up on the 'whys', there is too much going on for our simplistic dynamics to understand!
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