Robby Robertson robbed his (brothers) band members of songwriting credits. This is common knowledge. Levon Helm was always very angry about this. Rick Danko less so. Robby claimed 100% songwriting on many Band tunes, that were really co-authored, when the other guys were too stoned (heroin) to do anything about it.
Helm hated his guts!
As far as the Police go, when you are a trio you are practically living on top of each other. You cannot avoid anyone. So of course Summers and the drummer Stewart Copeland contributed to the tunes Sting claimed sole authorship for.
Yes, I should have said that even though the DVD depicted The Band’s songs very much as group efforts, Robby Robertson did get almost all of the official songwriting credit. They’re all gone now, but that DVD would have been a good courtroom exhibit in a suit over songwriting credits.