As far as I know, Any team can't tell England their player is injured and can't play, the FA changed the rules that only their medics can make that call.
Rodgers can't be called for 'letting him go'
The serious issue here is a player wanting to play for the National team knowing he isn't fully fit, and not giving a fuck about the team that pays his wages, if he aggravated the injury and weakened Liverpool with a month or more out, costing us a European place or maybe even the title, that is unacceptable