I told you already: during creation of an archive the -p flag has no any meaning. Tar always stores permissions, owner/group information inside the archive.
You can check it using: tar tvf <tarfile>.
The flags -p, --no-same-permissions, --no-same-owner and similar will only describe how tar tries to restore the original permissions/ownership.
These attributes will be restored according to the rights of the current user (so root will be able to restore everything, but regular users are not allowed to do that).
Also you can specify if umask should or should not be taken into account.

It's strange that the man page implies that it does, along with every tutorial and forum post I've been reading. That said, what is actually happening when I test things out agrees with you.

So the question remains, can tar be used in such a way that extracted files do not have their execute bit set?

that was already answered, tar itself cannot handle it. You have 3 options:
1. modify files/permission before you create the archive
2. modify files/permissions after extraction
3. use umask, but you can use only one umask settings for both files and directories (so if you want to remove x, you will remove it from dirs too)
4. bonus: reimplement tar (probably you can take perl/python/whatever module, not only the original c code)