Wait that doesn't sound right. Unless H1B legislation changed drastically since I had one, you cannot change jobs "safely" on a H1B. You can change job if your new employer files a petition to hire you. This petition is almost always approved and not impacted by the CAP, but you need it to work for them.

Again, I'm not a lawyer and I was on this visa more than 10 years ago, so maybe a lot has changed since then. Can you link to official documentation explaining this?