For AVI files Vegas uses Video for Windows. It does not use it's own internal codecs for AVI files. You will need to install an AVC Video for Windows codec to read these files.
AVC in AVI files is a little unusual, but it comes up at times. You could re-mux the AVI file, using Avidemux or similar, into an MP4 and that should work and then you can avoid the codec hell that can be AVI.
I'm just learning how to use ffmpeg myself so don't ask! It just happens that by coincidence I have the same problem. The converted file will have the original h264 stream and an AAC audio stream, and Vegas 12 Pro recognises this as "Sony AVC".