It is absolutely how it works.

“There are reinfections, but it is unlikely that -- if you mounted a good immune response -- at least over a period of several months, it is extremely unlikely that you will be reinfected with the same variant,” Anthony Fauci, the director of the National Institute of Allergy and Infectious Diseases, said in a press briefing on Friday.

If you factor in various other factors such as my vaccination plus booster, and the fact that I showed quite a bit of resistance to omicron even before getting it (took a week of habitation with an infected person before it got past my immune system), the risk of my catching and then spreading it is so utterly small that it is effectively none when it comes to risk management decisions. If I were that risk averse, I simply wouldn't travel by plane or car anyway.