In any case, its not a fact that any farmer has healthier animals because he uses straw instead of rushes. In any case of calf welfare that you mention, the problem is that the farmer isn't using enough bedding (regardless of the type) to keep calves clean and dry.
We calve 60+ cows here. Average winter in the shed is 6 month +. Calves spend more time in bedded creep areas than the average calf across the country. We have a pretty respectable calf health record that I won't detail here but can detail for you in a pm if you don't believe me. We bed with rushes and more rushes and always ensure that the calf never has to lie in any type of dampness. Its a brilliant source of bedding that breaks down and composts easily if you follow some basic principles when using it. Bale for bale, it won't go as far as straw, but its a free aside from the cost of baling.