So based on the above you have eliminated as a possible cause his dock and his cables, leaving just his PC and the hard drive itself.
You didn't specifically say his drive and dock on your PC doesn't work (I don't think), but I assume that it doesn't, as you have checked all possible hardware combinations.
Out of interest, what about one of your hard drives in your dock, on his PC? That should work, but given this issue I would not expect it to work.
What about one of your drives in his dock, on his PC?
The dock being exactly the same doesn't matter, if one has a fault.
I don't think updating the firmware on his SSD will change anything. But I would do it anyway. Firmware upgrades on SSDs do tend to improve functionality, performance, or reliability.
I was thinking maybe if it is a USB3.0 dock that interference may be an issue, or the heavy case could be radiating an EMF signal, but that would just cause data errors, not make the drive unrecognised and requiring formatting.
Anyway, I am now thinking either it is a very weird hardware issue in either the PC, drive, or dock, or it is something in the BIOS on his PC, or yours. I'm going with BIOS, unless testing the above combinations reveals something weird.
So, the drive is formatted with a GPT partition. Typically that requires the correct capability in the BIOS on his PC. I can't remember exactly what settings I have seen in my BIOSs (traditional and UEFI), but I think at least one had a setting enabling the use of GPT drives. It may have been labelled "Supporting large hard drives" or similar.
Just a thought as well. You said his drive was formatted as a GPT drive. Can your PC read a GPT drive? Do you use GPT drives? The fact that your PC detected the drive hardware fine, but wanted to format it does actually point to a problem with your PC reading GPT formatted drives.
http://msdn.microsoft.com/en-us/library/windows/hardware/dn640535(v=vs.85).aspxThere are also potential issues with settings for support of legacy USB devices under a UEFI based PC. If his PC has legacy support turned on, and yours has it set to Auto, or Off, perhaps this would make a difference. Maybe his PC is writing to the drive as if it is a legacy device, and yours only expects a non-legacy device?
Do you both have UEFI based motherboards, and do you have AHCI Mode turned on?
I suggest comparing your BIOS/UEFI settings to his, to see if there is something obviously different.