Must Time Machine backups be run while logged into admin account?

I have two questions, one simple, one deeper.

I've always logged into the admin account on my Mac to install software and run manual backups. I thought admin account permissions might be necessary to get a complete backup, so I've never tried using my standard user account to run a backup.

1. Does the Time Machine rely on user account status/permissions to be able to access & backup all the files on the disk?

2. If it is OK to run a backup while logged into a standard account, would the keychain files that are backed up be any different than a backup created by the admin account? I have a problem using a TM Backup to set up my new laptop. One Apple support agent suggested my problem might be solved if I ran TM backup while logged into that standard account. I don't want to do that if it makes a mess of my back-up disk. My guess is TM backup uses full pathnames to back up files, so would result in no confusion, but also no difference in what gets backed up.

Thanks,

Eric