Refactor the code that creates the list of secondary accounts

BUG=331805
TEST=No visible change. Existing unit tests.

Review URL: https://codereview.chromium.org/128513002

git-svn-id: svn://svn.chromium.org/chrome/trunk/src@243712 0039d316-1c4b-4281-b951-d872f2087c98
SVN changes up to revision 243712