Needless to say, my friend had his pasport taken by a machine gun toting policeman who then required him to pay the fine in the Police van before he could leave. My friend certainly did leave - he left Austria right then and there and spent the rest of his time anywhere but Austria.
An Austrian has emailed me stating:
This sticker is only needed on the Highways/Freeways ("Autobahn" here in Austria). Your friend ... hasn't read the signs which are placed at the borders. (Big Red Signs 4 meters high / 2 meters width). .... But normally the police in border-areas are very friendly and if you explain them the mistake of not (knowing) buying the sticker (the sticker costs 5 Euro / Dollars for 10 Days) they give you a warning , but not a 120 Euro ticket.
My only conclusion is that the police were doing exactly what the police over here do - selective, strict, enforcement of laws to collect revenue.
On this trip we found it very strange that the roads were always in the valleys.
Why became very clear in Switzerland and northern France. It's very hard to
take roads over mountains to get to the next valley. So the roads follow the
rivers and valleys until a sufficiently low mountain pass can be found - that or
a tunnel made thru the mountain.