Many addons affect physgun, and it's quite likely even gamemodes affect physgun. (I know little of Clockwork)
Though we try to remain gamemode and addon agnostic, due to the physgun being a large integral part of Gmod having, honestly, little to do with administration of a server, it's possible and likely the low priority control of physgun we attempt is getting overwritten.
From server console, while both a higher level group person and an admin that 'can pickup higher levels' are connected, please run "ulx debuginfo"
The server will tell you a location of a file to attach to your next post using the "Attachments and other options" link when posting.
If your 'lower' access groups can perform other ulx only functions on higher access groups, and you can give us an example or two of those exact commands (ie, ulx slap), we can look at the file and perhaps better determine why it's not working.
We may also be able to determine why physgun isn't workiing, but, as it's an often modified tool, it may not be as easy.