Huey is an interesting dude, his first band Clover used to open for and pal around with Thin Lizzy. He and Phil Lynott became good friends in which Phil kinda became his mentor. Huey also jammed with them live many times. Clover's first two albums were produced by a young Mutt Lange.
Huey and the band would eventually start helping with what was supposed to be Lynott's third solo album in '85 but drugs had taken their toll and Phil passed.
Here's a picture of Clover with Huey on the far left with the stache and John McFee of Doobie Brother fame on the right. Some of the band would go onto form Huey Lewis and the news and the lead singer of Clover wrote the hit 867-5309/ Jenny, and several other hits for Huey Lewis, Pat Benatar and others. Clover also did all the music for Elvis Costello's debut album as well.
Bottom line is by the time Huey Lewis and the News hit, most of them were very seasoned musicians and why they sound as good as they do.