This has become a bit of an experiment for me... the developer side of me wants to start jumping into some sourcecode.
The fact that all of the mothers had a single birth when I was playing them, versus them having twins each and every time they were unattended seems to be different from the original reported bug of there being twins born consistently in active families. Almost seems they've fixed it in one part, but not in the other.
The 6 mothers have all given birth again. 5 of them gave birth to twins, the 6th had triplets. With the exception of the mother that had triplets, they all had 1 baby (the same gender as the first born of the twins) when they were being played by myself, but twins when they "phoned in the birth". The mother with triplets had twins when I played her and triplets when I didn't.
Based off all these numbers, it's almost like it's automatically adding 1 additional child when the child is born while the mother is inactive. I would say that it's possible the percentage chance of the mother giving birth to twins is higher when the mother is not being controlled, but the fact that they've all had at least twins thus far, suggests there might be something else going on.
I took your advice and tried a different couple. They were boyfriend/girlfriend and lived in different households, when she had the birth by herself, she had twins. When I controlled her, it was only one child. So it seems to be repeatable across all Sims, old and new -- the father I've been testing with was created this past weekend. This testing couple I created weeks ago.
I took the original married couple who I first seen have twins (boy/girl) and had them try for baby too. I used cheats to level up the doctor of the house and she said the baby was going to be a boy, but didn't say anything about it being a multiple birth. The mother gave birth and she had twins again, two boys this time. I reverted to a save and tried a second time and she had twins again, both at home. I tried sending her to a hospital the third time unaccompanied and I got the prompt that she had twins. I went with her the 4th time to the hospital and still had twins. I even tried sending the dad to the gym for 14 hours after she went into labor and she never called with an update, but popped out the twins as soon as he returned home.
None of these Sims have the Fertile trait (it's never been necessary for me to consider even taking it). It seems to mainly be a problem with one Sim having a child with a Sim from a different Household and the player not actively controlling the pregnant mother. I tried having the father Sim be there for the birth of the children, but that woman won't pop them out while he's there.
I also noticed that an active Sim seems to give birth after around 3 game days. Whereas a pregnant Sim that isn't being controlled has the baby in about 1 in a half. I'm not sure if that matters, but thought I'd report it if it does.