calibre tests if a partition is readonly on linux by actually trying to write a file to it. So if it thinks your READER partition is readonly it is because either:
1) It is readonly
2) It has filesystem errors
3) It has incorrect permissions that prevent writing of files in the root directory
4) It is formatted as FAT32 and has reached the max number of files allowed in the root directory
ANd you can get more detail on the device detection process by running
calibre-debug -d
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