Not sure what the difference between your machine and your fellow colleagues machines are, but what I can say is that the dropdown in Git Extensions (the one that by default is located between the repository dropdown and the stash button in the menubar) will only show you the branches that you have available locally along with an option in the bottom to check out some other branch ("Checkout branch Ctrl+.").
Selecting the bottom-most option ("Checkout branch") will give you a dialog where you can select which branch you wish to check out. By default this one will also only show you the branches you have available locally, but now you can select the radio button for "Remote branch". The dropdown below that radio button will now show you all branches available on the remote repository (most likely called "origin"). Select the branch you're interested in and leave the rest of the textboxes and click "Checkout". Now you should be all set to work with the newly created local branch based on the remote branch you wanted to work with.