Sorry for not making that clearer, they are correct.
The potential disadvantage of doing it my way (through purchases only) is that it does take time to come back into balance, especially when your investments are large. That's probably only important when you're getting close to retirement, if ever.
For example, the latest drop shifted my asset allocation from 85% stocks / 15% bonds in September (last time I checked) to 75% stocks / 25% bonds now. I would need to buy stocks worth about 20% of my current savings to rebalance through purchasing only.
The advantage of rebalancing through purchases only is avoiding capital gains taxes on sales if you have to sell holdings that are in a taxable account. Tax-advantaged accounts aren't subject to rebalancing.
The other advantage is dollar-cost-averaging rather than lump sum purchases. For example, when do I rebalance given the current volatility? Now? Exactly on December 31st? (Again doesn't matter in long run, but can make us jittery). For me, the answer is over the next ~6 months, and the jitteriness / urge to market-time is automatically avoided. It's just another way of enforcing discipline and making it seem more like a long-term investment instead of a roller coaster.