It's simply that your cousin has 3 kids. By this point, she no longer cares who holds her kids so she forgets that 1st time moms don't like other people holding their babies.
I was always pretty willing to let anyone hold my first, but now, heck, I pass Scarlett off to whoever will take her!

She's been hanging out at my older kids' school this week while I am volunteering for the annual art show and pretty much every parent who is helping out has held her this week. She even had a group of toddlers in underwear (they're potty-training the 18 months-3yo class) surrounding her on her playmat and she was thrilled to have the audience.
I don't routinely pass her off to kids, nor would I ask my kids if they want to hold someone else's baby, but I do let my 3yo and 6yo hold Scarlett. I sit with them, but whenever they want to hold her I typically say yes (exceptions being if she's crying, hungry, tired, whatever). Some of my kids' friends have asked to hold her and I oblige their requests as well. And my SIL's 3rd kid is 9 months older than Scarlett and she lets my kids hold her and has let her 8yo carry her around since she was 4 months old.
Also, I find that many of my friends who have more than 1 kid are more willing to just pick up Scarlett without asking, probably cause they remember appreciating the help when their youngest was a baby. With the first, you never really mind holding them all the time, and not that you do with the 2nd and 3rd, but you're just constantly holding someone so the break is more welcome. When someone holds Scarlett, and the others need something, I can actually attend to them without having a baby in their face.
Oh, one more thing, I find Scarlett is always in her carseat, which was never the case with my first. So whenever I can hold her I do, but if I can't, and someone else wants to, I figure she appreciates the break from her seat. So she might be thinking back to when her youngest was an infant and how she was probably trapped in the carseat too, forgetting that you don't have to shuttle her around with older siblings.
So I doubt she meant any harm, she's just used to being a mom of 3!