They would have had you under a microscope looking for opportunities to ding you on family related items (phone calls, e-mails, emergencies). I am surprised that they actually told you that is why they didn't choose you (it's a foul to ask about those things in an interview, it's a foul to make decisions based on those things, and foul to tell you). They could have just said no.
Think of this as a positive learning experience and an elimination of future tension.
Me-45 W-44 S21, S18, D15 T-27, M-21 BD Jan 2014 PA revealed March 2014 In-house separation - April 2015 I filed - Aug 2015 She moved out Oct 2015