I spoke this morning with Scott, a supervisor in customer service. He said that, as everyone thought, it doesn't matter if you qualify before or after June 15th unless you are doing a challenge. He thinks that the agent who provided the misinformation was confusing regular qualification with challenge qualification. Unfortunately, there are now at least 2 people who answer questions at the gold desk who are misinformed and may pass the misinformation on.
BTW, he also gave on or about June 11th for the next DQM date and guessed that only miles thru a date a couple of weeks prior to that would be dealt with at that time.