The with statement does not appear to take opDispatch into account:
----
struct Foo {
    string[string] strs;
    void opDispatch(string s, T)(T t) {}
}

void main()
{
    Foo f;
    f.check(1);
    with(f) {
        check(2);
    }
}
-----
test.d(11): Error: undefined identifier check

Using dmd 2.062.