Whoever told you it's impossible in .NET is probably wrong. Don't you have interfaces in C# ? But you don't even need interfaces. Strictly speaking, unless you use typeclasses with polymorphic recursion, you don't need a runtime representation for typeclasses at all.
I think brianberns is probably referring to this: https://visualstudio.uservoice.com/forums/121579-visual-stud...
I understand the Haskell communities desire for coherent typeclasses, but I still find the newtype work around cludge to allow multiple implementation of, say, Monoid to be quasi hacky. What's worse, you can still fairly easily define multiple instances of the same typeclass accidentally (orphan instances) and the compiler won't catch it.