Unfortunatley for her husband the mommy will always threaten taking the child or children away... even if things are going PERFECT in everyones life. I think it depends on their "time of month". Some moms are just "me centric", no matter what you do to facilitate their wants, when it SHOULD be about the child's wants and needs.
Your sister should begin documenting every incident that happens in their care. She could keep it in a journal form. I keep records of every thing that happens with my Fiancee's children.. I keep records of their doctors appointments, school plays, their dance and piano lessons, I keep records of all events in their lives. It's a really neat thing to look back on as well. Do you think she would do something like that? I keep copies of all e-mails and I make notes of all phone conversations with the kids mom too. Things come up all the time with kids. Our communication lines stay open all the time.
I have a four year old so I'm trying to imagine that kind of story coming from her... I haven't actually been there but does he spank the child? Maybe that's what he's talking about. I'm not judging, mine gets a spanking when she's doing something she knows she isn't supposed to do. Kids are very exaggerating at that age as well, if you breathed on my sister when she was small, she'd cry uncontrollably and say that someone had hit her. :) lol, funny girl.
Otherwise, if you are SURE that nothing has happened, maybe the child needs to see a counselor to find out why he's telling such a lie. The problem is that if he tells this lie to a teacher (and it really isn't true) then there could be a lot of trouble for your sister and her family.