I have just purchased a Nexus 7 (2013) and it auto updated to android to 4.3 as I was setting up.
Unfortunately USB OTG now does not run. I purchased the Nexus 7 for it's OTG feature.
I've done a factory reset but it still loads 4.3
Is there any way I can go back to 4.2.2 - which does support OTG on the Nexus 7
I don't think the Nexus 7 (2013) ever had Android 4.2. I was going to suggest flashing a factory image but the only one available is Android 4.3 which suggests it's not possible.
As the other answers have suggested you will probably need to root to get the USB OTG functionality you are after.
If you are reverting to 4.2 only for USB OTG feature, then I would suggest you not.
I am using a rooted Nexus 7 (2012) from v4.1 - v4.3 and could say from that experience that it has to be rooted for the OTG features to run. Since that's missing from your question I assume that you are not rooted when you had 4.3.
The apps Stickmount and USB OTG Helper needs root privilege to run successfully.
You're going to have to revert by installing a custom recovery, and then flashing whichever ROM you require yourself. It's not difficult but needs to be handled very carefully (ie getting the correct rom, and following all the steps exactly) to avoid damaging your device. You may find it hard to claim repairs under warranty if you do this, depending on the laws where you live.
Device: Nexus 7
Can I upgrade my Nexus 7 to 4.3 via OTA, then re-root without losing data? I used a procedure of this sort to root originally, but I don't know if it is generally possible.
Note: I did not unlock the bootloader when I last rooted.
Updating from 4.2.2 to 4.3 will retain your data, but this will make you lose root. To root, you would need to unlock the bootloader, which will almost always require a Factory Reset (thus, you lose your data).
So, I suggest to back-up your user apps and data with Titanium Backup or something similar.