I know that as the contributor of the second point in your proposed dilemma, you may prefer crowdsourcing the right answer (I would suggest that this isn't a likely method for deriving an accurate understanding of this apparent dilemma) - but let me expand the original point, as there are further important facts to consider:
Now let's look at what the claimant from the first point gets wrong (it involves basic biology & energy metabolism):
Whether a cell undergoes anabolic processes (e.g., AA synthesis, lipogenesis, glycogenesis) versus catabolic processes (e.g., proteolysis, β-oxidation, glycogenolysis) depends on the energy state of the cell. The purpose of DNP is to, by uncoupling of oxidative phosphorylation, increase RMR (contributing to a substantial energy deficit). When the cell is in a negative energy state (i.e., caloric restriction/deficit + DNP; as is the universal use case for DNP), anabolic processes (building macromolecules, like proteins, triglycerides, etc.) are foregone. Instead, catabolic processes (breaking down macromolecules like proteins, triglycerides, etc.) are used to provide energy to synthesize ATP. Since this is frustrated by DNP (across the inner mitochondrial membrane, proton leakage occurs), the extraneous energy is released as heat (i.e., thermogenesis/increased body temperature). As such, the anabolic functions of insulin are irrelevant given the cell's energy state; and all that becomes relevant essentially are its anticatabolic features (at which androgens are far more useful because they preferentially serve to spare muscle protein, while serving as well to maintain free T, IGF-I [particularly with testosterone], etc. - that are all reduced substantially by caloric restriction).