Charging iPhone 13

False. Apple encourages using the old power adapters and cables. See the following from Buy iPhone 13 and iPhone 13 mini - Apple

As part of our efforts to reach our environmental goals, iPhone 13 and iPhone 13 mini do not include a power adapter or EarPods. Included in the box is a USB‑C to Lightning Cable that supports fast charging and is compatible with USB‑C power adapters and computer ports.

We encourage you to re‑use your current USB‑A to Lightning cables, power adapters, and headphones, which are compatible with these iPhone models. But if you need any new Apple power adapters or headphones, they are available for purchase.

False. It’s a ploy to sell you a charger that you don’t need. You can use any Apple or Apple approved MFI charger as long as the plugs fit without forcing. The speed of the charge will vary, but all power sources of 5 watts (1 amp) or more will charge any iPhone. Higher power sources will charge faster, but that’s the only difference.