Dear Jérôme,
I solved my problem with a new tomcat + basex installation/deployment.
Good news!
I always get a "read permission needed" with this kind of query (my db contains xml-tei documents):
[A] = http://localhost:8080/BaseX79/rest/mydb/mydoc.xml?query=//*:p%5B1]
Thanks for reporting this. I did some testing, and you are completely right, this is a bug. I will give you a note once this is fixed.
Christian