"It came as some surprise therefore, to be presented with a budget recording of the same piece by the same orchestra, but with another conductor. I really didn't get it. The music felt so alien to me as to constitute an entirely different experience."

There is an amazing amount of scope for different interpretations of course. Even different recordings of Stravinsky conducting his own music are dramatically different, showing that there isn't a single correct interpretation. Nevertheless classically trained musicians have a hard time if asked to play something different from the actual notes put in front of them.

You are right about Handel's "ad lib" too - but trained musicians have to learn how to 'ad lib' and it's quite a foreign skill to many of them.

In Handel's time and earlier, things were indeed much more like modern folk, jazz and pop music in some ways - the "figured bass" was the baroque equivalent of a guitar chord chart in that it showed you where the harmony was going while leaving the instrumentation and actual notes up to the musicians.