GnuCash 2.6.3 for Precise (via this PPA) ?

The official repos are not PPAs. The official repositorys are just that, repositories. PPA (personal package archive) are maintained by a person or persons online for their own use but are publicly available. There is a world of difference.

If you run:

sudo add-apt-repository ppa:mail6543210/gnucash
sudo apt-get update
sudo apt-get install gnucash

It will update.

"There is no technical differences between a repository and a PPA as far APT is concerned."
http://askubuntu.com/a/430583/16023

The ppa you refer to is "untrusted".
https://launchpad.net/~mail6543210/+archive/gnucash

 - Any "trusted", alternative ways of getting the latest GnuCash?

 - Can the "official Ubuntu repository" not be installed somehow?

 - Or via GnuCash directly, though "Most linux distributions come bundled with a version of GnuCash (...) it is recommended to use the GnuCash version that comes with your distribution.", i.e. "build from source" ?
http://www.gnucash.org/download.phtml

You seem not to be aware of the Ubuntu release philosophy.
Ubuntu is no rolling release. This implies that most of the packages stay on the version that was current at the time of release publication. A version upgrade is done only for specific packages (firefox, thunderbird, java, timezonedata ...), and in case that a bug fix solves a sever problem.

If you want to have a higher version of the standard gnucash 2.4.10 on precise you can

1. upgrade to a higher Ubuntu release (e.g. trusty 14.04 with gnucash 2.6.1-2)
2. use a PPA (with the restriction that there is only limited support on PPA versions)
3. request a backport of the trusty or utopic versions (you have to provide good reasoning that this would be required)
4. try building the 2.6.* version from source yourself

See also https://wiki.ubuntu.com/StableReleaseUpdates https://wiki.ubuntu.com/UbuntuBackports