I've updated to version 3.7.4 and this problem seems to be still there.
One solution - with a major security leak - is to allow anonymous users to edit their content and hide editing tools. But you can imagine that it would be nice to improve this as soon as possible.
The solution is to associate the edit priviledge for the first version of an object for users who can create these objects. But I don't know how to do this without modifing the kernel.
This issue was 'fixed' in 3.7alpha, half a year ago, but for reasons I do not understand has never made it into a released version of ez. I am running one site from svn/trunk as a result, which is far from ideal.
