I can't reproduce this locally. Henrik, can you paste your depot_tools/.git/config in this bug? 

Sure, here it is:

$ ./update_depot_tools 
Current branch master is up to date.

$ cat .git/config 
[core]
	repositoryformatversion = 0
	filemode = true
	bare = false
	logallrefupdates = true
[svn-remote "svn"]
	url = svn://svn.chromium.org/chrome
	fetch = trunk/tools/depot_tools:refs/remotes/origin/master
[rietveld]
	server = https://codereview.chromium.org
	cc = chromium-reviews@chromium.org
	viewvc-url = https://src.chromium.org/viewvc/chrome?view=rev&revision=
	project = depot_tools
[branch]
	autosetupmerge = always

git remote add origin https://chromium.googlesource.com/chromium/tools/depot_tools.git

should fix it.

Yeah this shouldn't be a thing that lots of people are seeing. Not having a remote origin configured at all is super non-standard.