Digging deeper, I remembered that this message has had some code changes around it. Most notable this, which was done by me.

The chang log tells me:

=head2 Changes in DBI 1.609 (svn r12816) 8th June 2009

  Fixes to DBD::File (H.Merijn Brand)
    added f_schema attribute
    table names case sensitive when quoted, insensitive when unquoted
    workaround a bug in SQL::Statement (temporary fix) related
      to the "You passed x parameters where y required" error
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That sure sounds related!

It is however nice to note the intertwined relations here. That change was submitted to DBD::File, but the code seems to have been moved to DBI::DBD::SqlEngine (see sub execute in that file) in more recent DBI versions. If you replace

  unless ((my $req_prm = $stmt->params ()) == (my $nparm = @$params)) 
+{
      my $msg = "You passed $nparm parameters where $req_prm required"
+;
      $sth->set_err ($DBI::stderr, $msg);
      return;
      }
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with

  unless ((my $req_prm = $stmt->params ()) == (my $nparm = @$params)) 
+{
      my $msg = "You passed $nparm parameters where $req_prm required"
+;
      warn $msg;
      }
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you essentially revert to what it was before 2009. Still wrong, but you might find a fix.

/me digs on. If I find something, I'll add that here.