The reason for the lifting of the ban was both for hunting tourism and allowing people to kill elephants that interfere with their livelihoods. If you're killing elephants because they might interfere with your farming, etc., I wouldn't expect to see their tusks removed.
I would imagine that hunters (who have already been issued permits to kill 60 elephants so far, see https://www.reuters.com/article/us-botswana-elephants/botswa... ) would take some part of the elephant as a trophy, so it probably isn't a result of the legal hunting permits.
Just to be pedantic and a bit conspiratorial, poaching is defined as the illegal hunting of an animal. Since lifting a ban on hunting elephants is definitely controversial, I would imagine it's in Botswana's government's interests to be specific in their wording. They've only "ruled out poaching as a reason," they haven't ruled out that these elephants were killed by people.