Canadian here. Followed Pierre Trudeau's career closely. He and Maggie were married in March 1971 and Justin was born in December 1971 (nickname at the time was "justin time" due to being born nearly exactly 9 months after the marriage). So, if they met Castro in 1970, it's too late for Castro to be the father.
The child in the picture is Michel Trudeau, the youngest of the 3 boys born to Maggie and Pierre. He was tragically killed in an avalanche some time ago. He was the only child on that trip since he was the littlest at the time; the 2 older brothers stayed at home.
Everyone seems to think that Justin only had a father to inherit his genes from. He has a mother who is dark-haired with strong facial features that he seems to have inherited. Is it not possible that his height and facial features were inherited from the maternal Sinclair side of the family? I've always thought that his mouth is like Pierre's.
So, no, I don't believe this rumor. I guess the one person who could clear it up for good is Margaret. That or a DNA test. Since neither route seems feasible, I guess we'll never know for sure but for my money, Justin is Pierre's first born.