Executables without shebang and vice versa

Among the many *.pike (and *.pmod!) files in the module directories there are a few marked as executable but missing a shebang (#!) line, and a few that has a shebang but are not executable. Which ones, if any, are meant to be executed directly? (I'm not talking about scripts that used in the build process, only ones that are installed.)

Since none are installed as general-purpose tools in $PATH, and since the ones in Tools.Standalone are meant to be run via pike -x, couldn't you simply delete all the shebangs (which, in case they read "#!/usr/local/bin/pike", are wrong anyway if pike isn't installed under /usr/local) and reset the x bits?