Or imagine a small width wedding band...it would be very small print 
This sounds like a different type of band than what I remember seeing placed on chicks (although I have very limited experience with this). Is this unusual? Are there specific places where they use these bands? It sounds like you would have to be actually holding the leg in your hand to be able to read it.
Jules' band is called a "ring band" or a "breeders band". Its not used on birds for release, rather birds in breeding programs or falconry birds. Until we know technically who she is and where she came from, we can only speculate on why she still has it on. A possible explanation is that she was a falconry bird or part of a breeding program and it was decided to release her and she wasn't given the coloured/aluminimum bands we put on all our birds. Could have been an accident, oversight or maybe she managed to escape during banding. The other explanation is that she's an escaped falconry bird, but many falconry birds (or maybe all of them now) have radio transmitters on them so that they can be tracked down by the falconer. Falconers spend alot of time care for and flying their birds on a daily basis so they take care to keep track of them in case they get into trouble.