There is no evidence that running on paths/grass etc is better for muscles/joints than roads/pavements. It would seem intuitively to be the case but is a myth.
It’s more pleasant though, running off road I mean. The whole ’causes less injuries thing’ is one of those running things that gets attributed to anything with equal dubiousness: viz, barefoot running shoes cause less injuries, stretching causes less injuries, drinking strawberry vodka causes less injuries etc.
The reality is that most regular runners seem to have regular injuries. I once went riding with someone who confessed that there was a regular evening riding group in his village comprised entirely of injured fell runners, which tells you everything you need to know about running 😉
Logically runners will grasp at anything that they’re told may reduce the chance of them injuring themselves, including bikes…