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The issue was created by rules.

I had read somewhere on two or three occasions that the Rules module could generate such error but I thought disabling the module would be enough to show if rules were involved or not. It didn't. Apparently, the rules are still active when the module is disabled (a diehard, at least in my case!)

I also had to disable the rules one by one until I found the culprit. It was a rule automatically making the new authenticated user a member of a welcome group. Somehow, the data in the rule had shifted and it was no longer the account but the site:logged-in-user that was made a member of the group.

The lesson here is about Rules and that the rules need to be disabled. Disabling the module alone is not enough. I hope this helps someone.