Update: Got the patch done on our PC - running 8.1 x64 fully updated. I didn’t feel safe using the pre-patched file, so I did it my own way with the help of the linked guide. Looking for the original bytes to patch, though, my version - updated on 4/2014 by Windows Update - didn’t have the full sequence of bytes. The pattern “0F 84 1B 70 00 00” at the end of the segment was different. But knowing how assembly code works, I patched over the different bytes with “90” anyway (as the instructions indicated), and the patch worked great.
In Windows 8, just like 7, Vista, and XP before it, SFC wants to protect the file. I had to take ownership of termsrv.dll through the file properties, then give Administrators “full control” (only read is given by default). Then, I ran an rundll32 to sfc_os.dll to disable SFC until reboot (I don’t want to totally disable SFC for this!), using “rundll32 sfc_files.dll SfcTerminateWatcherThread” which gave no errors, then renamed the old file to termsrv.dll.bak, and copied my patched termsrv.dll into System32. Rebooted, and I was able to log in from the laptop without logging off the user on the TV. 
So, basically:
- copy termsrv.dll to desktop
- use hex editor to locate “8B 81 38 06 00 00 39 81 3C 06”
- replace that, and the following bytes, with “B8 00 01 00 00 89 81 38 06 00 00 90 90 90 90 90 90 90” (do not expand the file)
- take ownership of termsrv.dll through Properties, and give Admins full control
- launch “rundll32 sfc_os.dll SfcTerminateWatcherThread”
- rename termsrv.dll to termsrv.dll.bak
- copy patched termsrv.dll from desktop to System32
- reboot
And done! 