They were wrong. 8.2 allows you to upgrade directly from 6.2.1 (but nothing earlier). FYI - there's no MM (Methodology Manager) in 8.2. So you would want to convert anything in MM to projects before upgrading. And it's never a bad idea to run the validate program (database folder) before upgrading.
Edit - last time I checked, the unattended scripts weren't working from 6.2.1. A ticket was submitted for them to fix, but I don't know if they did. So AFAIK, you will have to do the upgrades manually. That is, you need to to launch it and guide it through the process. ~20 minutes for an average sized database.
There are no issues following the upgrade path from 6.2.1 to 8.2, just make sure that you've run the validate schema tool before you commence your upgrade and again once you've completed the 8.2 upgrade.