That's incorrect. It's all forward and backwards compatible, although the speed might be an issue. There's nothing that will damage an iPhone by using a lower power source. Obviously a 5W cube provides 1/4 the maximum power as the 20W that the newer iPhones max out with when using a USB-C to Lightning cable. However, that won't damage a battery. I have no idea why anyone would say anything like that with no merit other than maybe trying to sell new accessories.
I still have an iPhone 7, but my family is using OEM and MFi USB-A to Lightning cables along with higher power USB-A power adapters and they've been doing just fine. If anything, they might be better for battery life, as slower charging inherently generates less heat. The benefit would be marginal though.
It's still effectively a single 3.7V nominal lithium-ion battery. Newer iPhones will take in 5V or 9V, and they end up converting it to a suitable charging voltage.