BadMom would totally lie on the reading log. I've got a voracious reader who goes through stages where she doesn't feel like reading. Or she feels like reading a particular *cough*PercyJackson*cough* book for the umpteenth time, picking out just her favorite parts. Or she feels like listening to a particular *cough*PercyJackson*cough* audiobook for the umpteenth time, picking out just her favorite parts.
I am not the Homework Police, and IMHO there's nothing that kills reading for pleasure like being forced to read it's not pleasurable. If the spirit of the reading requirement is to ensure basic literacy and establish a habit of reading for pleasure, and if my kid is literate and reads for pleasure when it's pleasurable, the spirit of the requirement's been met, and I consider the homework to be done.
BadMom has a bad attitude towards school. OTOH, I don't send in a sheet for the teacher to sign and send back weekly, saying that she actually explained fractions so the kids understand them, rather than teaching everything by rote. Or that she made sure my kid had ever heard her assigned spelling words spoken aloud, so when the other kid who gives them to her at test time totally mangles the pronunciation, my kid doesn't think, "oh, maybe I've been studying it wrong, and it's really pronounced that way, so I should spell it 'revelance,' not 'relevance.'" So they could be getting worse!
