(not a real answer, I expect to update it frequently as the situation develops)
Weird.
Yes, Developer Edition is a "Production" as far as connecting apps are concerned. You might have to file a Case with Salesforce Support (Help&Training link in the upper right corner).
Workbench does use API (and probably so does this Apigee thingie) but if you're using your username & pass I don't see how it might go to OAuth...
Can you download any other SF-related tooling (Data Loader, Force.com IDE, Real Force Explorer, Excel Connector, some iPad/Android app... hell, Chatter for Desktop even) and try the connectivity?
Sometimes API products don't display special field for the security token (which you can bypass by entering longer string in the password field: "passwordSecurityToken") but Workbench never asked for a token when I was accessing my Dev. Edition.