Resharper suggests parameter can be of type 'BaseType'

what are the benefits of using base types in method parameters?

Here's one sample:

private void Foo(List<int> numbers) //R# laments: parameter can be IEnumerable. 
{
    foreach (var i in numbers) {
        Console.WriteLine(i);
    }
}

And here's another one

public class Foo : ICloneable
{
    public object Clone()
    {
        return MemberwiseClone();
    }

    public Foo CopyMe(Foo other) //R# laments: parameter can be ICloneable
    { 
        return (Foo)other.Clone();
    }
}

...where we can change the type and anything but Foo will fail at runtime.

So the question: what should I do when R# suggests parameter can be of type 'X'?

PS. Just another explanation for Whysharper - a plugin that dovetails Resharper and StackOverflow. People say it's nice but lacks good explanations - hopefully together we can make it better ;).