I expect by now you've seen Shane's reply about the same article on the 'Memories of Stonesfield' Facebook page. In case not, see this earlier thread on the messageboard where I asked a very similar question after finding the very same newspaper report:
NB the above thread includes a link to a photograph of some of the Stonesfield band members in Finstock, in around 1900. It's interesting to compare that photo with one of the wonderfully named "Rackety Band" which has been posted on the Facebook page very recently, with names of the band members. I reckon they must be of a very similar date. From the "Rackety Band" photo we know the Stonesfield band had elaborate frogging on their uniforms, and sashes, which makes them easy to pick out in the larger group photo at Finstock.
If I remember rightly, the band's founder, Joseph/Job Oliver (who perhaps found it hard to settle after his military career?), later disappeared from Stonesfield: he pops up again in Gloucestershire in some criminal records. I forget the exact date - early 20th century? - or exactly what he'd done, but do remember that he was of no fixed abode at the time. I don't know if the band survived without him. Maybe when more post-1900 Oxfordshire newspapers are online we will be able to fill in more of the story.