Used to be true, not any more. But you CAN transfer to AAdvantage. Diners Club is also owned by Citigroup, but has their own customer service staff, and is generally much better than Citicards.

One downside is that there is a charge for transferring points. I transferred a couple hundred thousand miles to UA when UA still participated in the Diners program a year or so ago, and I think the charge was around $100.