I'm not sure if you commented on the wrong issue accidentally but what you describe is not related to this issue. It is quite possible to start a Minecraft server without an Internet connection. It is also possible to connect to it as long as the username that you use in offline mode is not longer than sixteen characters.
This issue exists in 1.5.2. Steps to reproduce:
Start the Minecraft launcher.
Enter a username longer than 16 characters. I used "abcdefghijklmnopqrstuvwxyz".
Enter any password.
Click Login. The login will fail. Click "Play Offline".
Start a server in offline mode.
Attempt to connect to it.
This is still valid in the 1.4.5 release. However, the exception I recieved is:
java.io.IOException: Received string length longer than maximum allowed (24 > 16)
at net.minecraft.server.Packet.a(SourceFile:236)
at net.minecraft.server.Packet2Handshake.a(SourceFile:30)
at net.minecraft.server.Packet.a(SourceFile:193)
at net.minecraft.server.NetworkManager.i(SourceFile:249)
at net.minecraft.server.NetworkManager.c(SourceFile:15)
at net.minecraft.server.NetworkReaderThread.run(SourceFile:93)
EDIT: Just realized I posted the de-obfuscated stack trace. Either way, the error is the same. I can additionally post the obfuscated one, if desired.
EDIT2: More information is always better! Here's the obfuscated stack trace.
java.io.IOException: Received string length longer than maximum allowed (24 > 16)
at eg.a(SourceFile:236)
at cz.a(SourceFile:30)
at eg.a(SourceFile:193)
at cg.i(SourceFile:249)
at cg.c(SourceFile:15)
at ch.run(SourceFile:93)
Closed with no explanation?