It might smell like BS to you, but for the right person, both are absolutely not BS.
For example I have kids that I am the primary caregiver for. My wife is in a residency, so she can't be relied upon for child care. Therefore I cannot leave for work before the kids are in school, and I must return from work in time to relieve them from the childcare arrangements I have for them after school. No matter what is happening in my job, I have to do this. You cannot send me away on multi-day trips to a conference because I can't go. I can't stay for an emergency at work. My primary obligation is to my children.
Depending on the job this could be a minor detail, or an absolute deal breaker. Certainly it is something that I will need to have any potential employer be aware of and OK with. If that will be an issue, it is important that it be sorted out in the interview.
If you hear this in an interview and it still sounds like BS to you, I've done us both a favor. You won't hire me for a job I shouldn't be in. Because everything that I said is absolutely true.