The assertion is not correct, viruses do not need to spread to new hosts to experience meaningful mutation.
If RNA is damaged and changed and the virus particle is destroyed or for some reason never replicates, I don't count that as mutating, but then again what do I know.
There are mechanisms for bacteria to uptake dna in the environment and incorporate it (e.g. antibiotic resistance). But without replication of the bacteria the resistance wont spread.
One interesting point is that in general biology they teach that lamarckian evolution doesnt exist, but bacterial uptake of DNA demonstrates that it does exist.
The Sars-CoV-2 virus (provisionally) doesn't seem to infect and then suppress only to re-emerge later in a new infection, or hang around as an active infection for months. People get sick and their illness lasts a big armful of days.