On CC and COI - I agree with those who are pointing out the limitations of the "anti" studies quoted. It seems they are talking about children crying for really excessively long periods of time, not properly managed CC/COI. If you're leaving a child to cry for THAT long...you're doing it wrong, or something else is wrong. And 14 weeks is, imo, rather young to be thinking of CIO. Not to mention "being naughty", ffs, what a ridiculous idea.
As you've guessed, I'm generally pro COI, it worked well for us and was the only solution in the end to DS's sleep disruption after moving house last year (he was about 18m at the time). And he's one of the happiest kids you'll ever meet, and perfectly well bonded to me and his dad.
But more importantly, useful (hopefully) advice for OP: everyone parents differently and as others have said, everyone's got a bloody opinion about whatever you happen to be doing that's different to them. Sod the lot of them. They are not you, they will never know or love your children like you do, and by definition you, as your child's mother, are infinitely better qualified than they will ever be to decide what works best for your children and your family overall.
CC/CIO is not for everyone. In the end it really doesn't matter how you manage your child's sleep, as long as whatever you do works for you, the child and the rest of your household. I think the biggest problems tend to come if you're trying to follow a regime you're not totally comfortable with. So follow your own wishes and as I say, sod anyone who disagrees. It's your call.
Having said that, the vast majority of the people who are encouraging you to CIO mean well and want to help you (I do mean the people you are close to rather than random women in the street, WTF was SHE on?). They are giving the advice because they genuinely think you'd be happier if you followed it. It's basically well-meaning, but unfortunately somewhat ignorant behaviour from people who don't understand that you can't simply change your own parenting style just like that.
I have a friend whose well-meaning friends literally dragged her on a girls' night out when her pfb was 8 weeks old. She had never left him before and hated every moment away from him. Nine years later, it still pains her and she resents those friends for thinking they knew better than her what would make her happy. And yet they absolutely meant it all for the best.
Last thing (promise!) - feel free to imagine choke-slamming anyone who airily tells you to "just rely on your maternal instincts!". Maternal instinct is powerful and mighty, but it is sometimes not realised, I think, that it does not quite arrive fully-formed. All it means in the beginning is that you love your child beyond all reason and would do anything - and go through anybody - to protect them. It doesn't mean you will always know exactly what to do with them. It certainly doesn't mean you'll be able to effortlessly interpret every single cry. A lot of that comes with experience, but kids still constantly throw new things at you. Personally, I got a lot happier when I was able to admit to myself that I didn't always know just what to do, and shouldn't expect that from myself.
Apologies for excessive length. Hope it's remotely helpful at least. All the very best to you.