Cron – User crontab not accessible

I cannot edit my user crontab without being superuser.

I expected the following to work, but I get an error message:

$ crontab -e
crontabs/gauthier/: fdopen: Permission denied

The following is working, but I don't think I should need sudo to edit my user-specific crontab:

$ sudo crontab -u gauthier -e

The permissions on my user crontab:

$ sudo ls -l /var/spool/cron/crontabs
total 4
-rw------- 1 1001 crontab 1139 Sep 10 08:36 gauthier

I tried adding myself to the crontab group, to no av (I understand now that I shouldn't be in that group, it's only for SGID to work).

An answer to this question says to change the permissions, owner, and group of /usr/bin/crontab, but that file does not seem involved here. And I don't see why these permissions would have changed from system defaults.

Where am I wrong? Is it normal that crontab -e doesn't work? Even if I am in the crontab group? What should I do instead? If I need to change the permissions and owner of /usr/bin/crontab, why aren't they working in the default installation?