His comments are based on fear-mongering he read somewhere or an overly-literal interpretation of terms and conditions written to cover the ISP's ass in every theoretical situation possible.

ISPs who enforce data caps already priced it in and technically have an incentive for you to exceed your cap as fast as possible so you pay to increase said cap (they can however still slow down your traffic as they wish, to ensure sufficient capacity for everyone).

ISPs who don't enforce a cap actually still internally enforce a reasonable cap of several terabytes at their discretion. And of course, they can and will use traffic shaping to ensure the integrity of their network so your usage doesn't affect others. If you exceed that soft cap consistently several months in a row they may get in touch, but other than that you're fine.

TLDR: host your server and enjoy. When you get to the scale of the next YouTube, then you have to worry.