Citation needed. I've never once seen any solid data to support this argument. Let's calculate exactly what you're missing out on by drinking RO water as opposed to tap water. The average TDS of US tap water varies, but the EPA specifies a max level of 500 mg/L in their secondary standards literature. Let's assume that you have 500 ppm TDS in your tap water, and that you actually drink your tap water (lots of people don't). The average person needs to drink about 3L of water per day. If your tap water is 500 mg/L, you're consuming 1,500 mg of solids per day from your water. So, by consuming deionized water instead of tap water, you're missing out on 1.5 grams of Ca, Mg, Na and other ions commonly present in tap water. So the argument is that by missing out on 1.5 grams of Mg and Ca from tap water, your body is going to be robbed of minerals? I don't buy it.
This argument also doesn't make sense when you consider that your stomach is primarily full of hydrochloric acid, among other things. Since HCl is many orders of magnitude more acidic than purified water, shouldn't you be concerned about the vat of acid sitting inside your body?*
* - rhetorical. No, you should not. Your pancreas produces bicarbonate to neutralize any stomach acid that makes its way out of the stomach. This bicarbonate and other foods you eat will be more than enough to replace the 1.5 grams of solids you're "missing" because you're drinking purified water.