Thanks for the hint 
I can see, that internally near() does the same as my last example:
> near
function (x, y, tol = .Machine$double.eps^0.5)
{
abs(x - y) < tol
}
<environment: namespace:dplyr>
Where
> .Machine$double.eps^0.5
[1] 1.490116e-08
So using a tolerance of 1.5e-08, rather than the 1e-10 in my example 