First, the insured has to be legally responsible for the bodily injury. In a case such as this, the insured may be held legally responsible because he took no action to get rid of the mold, or because as the owner of the building, he is strictly liable for the condition of the building being the cause of harm to someone; this is a legal issue that we cannot answer. But, if the insured is held responsible for the injuries, that leads to the second problem.

The pollution exclusion can be used to deny coverage for a bodily injury claim. Mold and fungi can fit the definition of a pollutant since they are irritants and contaminants. And, the injury would arise from the discharge or escape of the pollutant from premises owned by the insured. This situation is what the pollution exclusion addresses. It is true that mold and fungi are not specifically mentioned in the pollution exclusion but there is an endorsement that allows the insured to buy back some limited coverage for fungi or bacteria exposure, so the intent is there to exclude such coverage under the standard CGL form.

Based on these problems, a claim against the insured could very reasonably be denied by an insurer.