There was a tweet that was put out only a few days ago which showed a beta tester opening their weekly chest after doing 15 M+ runs and getting 3 necks as their choices. So, at least as recently as then, you can still absolutely get duplicate choices in the chest. So it seems that it is Blizzard who are lying.
If you can still get a choice of a slot which is 'filled', then that means that even a 5-6 month estimate may be off, as it would only take a couple of dupes to throw that completely out of whack.
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You only get those 3 choices if you clear 10 +15s per week. You must also factor in the necessary clears to upgrade your key to that level. That is a lot of time spent doing nothing but M+.