You can fly in low to no viability with an IFR clearance.

I haven’t taken IFR classes but my guess is he either violated the glide scope via an incorrectly set barometer (either overloaded by what he needed to be done, misheard the ATIS, ATC didn’t give correct barometer reading to use, or just a mistake in setting it), or because he went below the decision altitude to fly the missed approach.

He could have done things he shouldn’t have done, but flying in dense fog is not one of them