Let's look at that a little more closely, shall we? A. Pay $56M for a service company that is not profitable, has very little marketshare, and may be out of business in the very near future. B. Pay $3B for product company that is highly profitable (most profitable in it's segment), has great marketshare (largest in it's segment), has huge brand recognition, and could pay for itself within the next 2-4 years.
Warren Buffet might not have signed off on the Beats acquisition, but I'd put money on the fact that he'd sign off on it 10x out of 10 before he signed off on Tidal.