Follow up - Job Interview Went Well!

You can ask, but I wouldn't. Your new boss is doing this as a courtesy to your old boss. It's business, plain and simple.
Imagine new boss granting your request and a month or so down the line the new boss gets a call from old boss saying "What the hell, you stole my employee...!"
You taking the new job will not reflect negatively on you, if that is your concern. You are trying keep it all friendly, I get that. But it's BUSINESS.
So, let the new boss make the call and it will be all good.
And congrats!!!!!

I would leave it alone and let them reach out whenever they feel like it. Your new company has already said that they know your old company cuts dead weight quickly so they knew you must be a good employee. Surely they will be able to take whatever is said with a grain of salt. It's not like they're calling for a reference. You've already been offered the job. No matter what the former employer says, you will quickly be able to show them who and what you really are.

I wouldn't. You are going to have to prove yourself at the new company either way, whether things are said about you or not. There's no reason to put your new boss in an akward position. Plus by asking, you make it seem as though you are afraid she will find out something about you.

Added after your SWH - If what you detail here is the way it is, I'm sighing with relief for you. It does sound like they won't send you packing the moment you give your notice. Will your new firm give you latitude on your start date according to how much notice your new firm needs?

Given that the SVP know's the CEO's style, I think that it might be okay to talk to her about your worries. Just remind her of what she said about the CEO first, and make sure somewhere in that conversation, you say gracious things about him too.

Original:

Are you 100% sure that this isn't kind of like calling them to get a "reference" on you to make sure that they've made the right decision offering you a job? It sounds like a sneaky, backdoor way to do this. I don't really understand why she wants to tell them that she didn't "poach" you. Why does this smooth the waters? What does it matter whether you reached out to them or whether you were approached?

I really don't like this and I am worried about you. I know you said she is a friend, but this sounds really fishy. You can take this as a red flag, or not, but I really think that this is improper.

If the CEO says anything nasty and you lose this job, you could sue him, but that doesn't help pay the bills while you go round and round in court.

Dawn

Yes, I think given the reasons you have stated in your post, it is reasonable to ask her to hold off on writing this letter.

I'd probably frame it as "no need, but thanks". And congrats to you on a successful job interview!