if safe_mode=On there is no possibility to obtain HTTP Authorization header, so no validation can be make.

The solution : why not include Authorization header in $_SERVER["Authorization"] ... ?

Sample code :
<?php
//phpinfo();

 if (isset($_SERVER["PHP_AUTH_USER"])) {
  echo $_SERVER["PHP_AUTH_USER"].":".$_SERVER["PHP_AUTH_PW"];
  print_r(apache_request_headers());
  phpinfo();
  exit;
 }

 if (!empty($_SERVER["REMOTE_IDENT"])) {
  echo $_SERVER["REMOTE_IDENT"];
  print_r(apache_request_headers());
  phpinfo();
  exit;
 }

 if (!empty($_SERVER["Authorization"])) {
  echo $_SERVER["Authorization"];
  print_r(apache_request_headers());
  phpinfo();
  exit;
 }

  Header( "HTTP/1.0 401 Unauthorized");
  Header( "WWW-Authenticate: Digest realm=\"www.horiaciker.sk\", opaque=\"opaque\", nonce=\"nonce\", stale=\"false\", qop=\"auth\"");
  Header( "WWW-Authenticate: Basic realm=\"www.horiaciker.sk\"", false);
  echo "K pr?stupu je potrebn? zada? platn? login a heslo\n";
  print_r(getallheaders());
  exit;
?>

if PHP is running as Apache module in safe_mode=On and I use "HTTP Digest Authorization",
 there is no possibility obtain supplied Authorization
header.

When I use apache_request_headers() function, Authorization header is not included (if safe_mode=On)!

So I can not authenticate request.

This is a explicit security feature to avoid stealing authentication data on shared environments.