I don't think your OP is clear either.
As I read it, she wandered off alone, bumped into him on the cycle path as he was walking his dog and walked with him for a bit before you found them.
She knows him, she has walked with him before, and she told him she was allowed to walk with him now. And he believed her because it's been true in the past.
And if that is the case, YABU.
You've obviously trusted him before. How did that work? Did he ask you in person if he could take her for the walks or did she just go to visit his daughter and go with them without you knowing until afterwards?
I can understand you were frightened, and I do believe that children should always, always ask their parents "is this alright?" before they go off with someone even if they know them well. But I think if she sneaked out, bumped into him and lied to him, you have been unreasonable.
Which direction were they walking in, away from home or back towards it?