I think the OP is entirely justified - he could equally ask for the band to learn songs that are not in their set that he knows well... Also he may not have loads of spare time/and or there are other difficult songs he likes that he could be learning..
I think someone in the band has read some management books and entirely misapplying some of the nastier interview techniques. My personal favourite was at Schlumberger many years ago where they took 6-8 candidates out to dinner and then asked them to explain in front of all the others why they were best suited to the job and why the others might not be,,