Actually, you've found it more precisely than you'd thought.
The EA documentation is quite vague on this, mentioning the attribute obliquely, and not defining it at all. Further, no list of values is given, nor is a source cited.
Like most values that EA provides in a list, the values here come from a set of 'allowable' values that EA keeps somewhere, perhaps hard-coded. In this case there are only three values. As you can guess, you've found them. And as you also can guess, the value "anything" is not among them.
[Now, if you find that attempting to set any value other than "none" (versus setting the value to a string of "anything") is causing the problem, you need to do some additional surgery. The actual value is stored as a string in either of the SourceChangeable or DestChangeable fields of t_connector. Each of these is VARCHAR(12) NULL. They may not be blank (versus null).
I thought this might go back to UML, but on checking the UML 2.1.1 standard (superstructure and infrastructure) I cannot find anything relevant.
[NOTE: That does not mean it is not there, just that I did not find it under a similar name. PUNDITS: Weigh in here as appropriate.]
So, let us know if you can set any of the strings from the Properties dialog - remember that they are likely case sensitive - or whether 'anything' other than the default screws up. We can certainly set the other values through the UI, and they definitely go into the database. [I know, I just checked this on build 826.]
HTH, David