Imagine another scenario - Aeroplane enters IMC. Pilot A (LHS) does not have an IR but pilot B (RHS) does. Are people really saying that Pilot B should sit back, and relax as the aeroplane plummets to the ground because he cannot become PIC in the air? I don't think so......
Of course not, PIC and handling pilot are not the same thing. No reason why A can't give B control while in IMC.