Check C++ class publicly inherits from template class with anonymous parameter

Similar to this question, how do I test that a class Impl publicly inherits from a template class BaseTempl (i.e. class Impl : public BaseTempl< ... >{ ... };), without specifying the template arguments?

Different from the aforementioned question, however, I would like the test to still compile (and return false) if the inheritance is not public.

Ideally, the code would allow me to do something like this:

class alpha : public BaseTempl< int >{};

class bravo : BaseTempl< int >{};

class charlie{};

class delta : public BaseTempl< int >, public charlie {};

class echo : public delta {};

int main(){
    publicly_inherits_from < alpha,   BaseTempl > (); // true
    publicly_inherits_from < bravo,   BaseTempl > (); // false
    publicly_inherits_from < charlie, BaseTempl > (); // false
    publicly_inherits_from < delta,   BaseTempl > (); // true
    publicly_inherits_from < echo,    BaseTempl > (); // true
}

The answer from the linked question gives the following error when I attempt to compile the above code:

error: ‘BaseTempl<int>’ is an inaccessible base of ‘bravo’