>>> The 2nd line of text had the word online which they didn't mention
They get hyper only when ONLINE is used in the title of the ad. Using ONLINE in the body of the ad is okay.
>>> I think its an automated process
I don't think it is automated - it is manually disapproved by editors. I feel the word is disabled on a case to case basis, after being checked by the editors. If they want to disapprove all the cases, they could easily do that during the ad creation process.
For example, when you try to insert the word "Google" into the title or the body of the ad, you won't be able to submit the ad. It is "instantly" disapproved.
>>> We had an e-mail back a little while saying it was fine to use it, so we redid them, and now they are disapproved again.
Forward the email to AdWords support again. This time ask the editors to add a comment to your account so that other editors don't dispprove it (According to customer support, they can add comments to individual accounts)