Earlier quoted context omitted.
This is just wrong (as you say, careless). The criteria is "metabolism", not growth and reproduction. Similarly, viruses are not alive although they can reproduce. Interestingly, there are some highly parasitic organisms with limited ability to metabolize, that is, they have lost their genes and instead depend on their host organism (but I think all those examples still have some level of metabolic capability).
I don't really know what "metabolism" means, abstractly. I am deader than a virus without chloroplasts existing elsewhere. Viruses need a host for the productive bit, I had food for the non-reproductive bit. Viruses don't break down fast enough compared to their abundance to cause extinction, so why fault them for optimizing? People commonly theorize that virus came from rump parasitic cells. I wouldn't be surprised…
Nowadays however it is more widely believed that eukaryota descend from archea, but anyway it's pretty much a given that viruses are not and have never been alive. And while the opposite has happened, gene transfer usually goes from viruses to cells, endowing them with new abilities, more than the opposite direction.