There is no harm in jail breaking a device that was updated to iOS 6.1 over-the-air (OTA). You didn't do anything wrong and the jail break will be fine.
The reason why we emphasized NOT using the OTA is because of a future potential re-restore option. A re-restore was created for iOS 5.1.1 a few months ago. A re-restore enable you to, well, re-restore iOS 5.1.1 in case you borked up your iPad so badly that the only way to fix it was to restore and put a fresh iOS on it. Without the re-restore option, the only choice was to upgrade to the iOS currently being signed by Apple - which was not jailbreakable. So, without the re-restore, people were out of luck if they messed up their iPads/jailbreaks.
However, due to how Apple changed the APTicket, the re-restore would not work on devices that has iOS 5.1.1 loaded from the factory or from an OTA. The only time the re-restore would work would be when the iOS was loaded on the iPad via iTunes (either the regular way or via shift/restore). A lot of us found this put the hard way...
There is no re-restore option (yet) for iOS 6.1. However, as a lesson learned, we are emphasizing not using the OTA option ... just in case.
Again, if your iPad was jail broken with an OTA-installed iOS 6.1, you are fine. However, in case a re-restore becomes available, you will want to restore and load iOS 6.1 on it - using iTunes, NOT the OTA method.
Hope this clarifies thing, a bit.
Marilyn