I haven't seen any research to support that contention -- rather, everything I've seen suggests you don't get coronaviruses like colds once off, so you don't "get it over with". Instead, they can weaken your immune system and these viruses can stay around for years, as discussed in the article.
The article is a mix of half-truths and speculation with a few random facts sprinkled in. It doesn't represent any sort of scientific consensus. Don't take it too seriously.
Infections with typical rhinoviruses and coronaviruses build adaptive immunity to those viruses (as well as those that are genetically similar). This typically reduces the severity of subsequent infections. They didn't stay around for years.
When we talk about things that "strengthen" or "weaken" the immune system that's really an oversimplification. There's a lot more going on in the complete system.
