Earlier quoted context omitted.
What do you mean by "dl the totp authenticator"? But the answer is no. Without the TOTP secret no one else can generate valid codes. If you sync your secrets to some cloud service then yes, you are trusting that cloud service. And if you let your TOTP cloud service reset your account with an email then it probably isn't the most secure option. But the important thing here is that the user is in control. They can memo…
I meant “download the totp generator”. Correct me if I’m wrong but the totp generator has to linked with some account, the security of which is not managed by you, and is just as vulnerable as that account
As such, no, it's not associated with anything from the source account. It is not challenge/response, and you can scan the QR code with 10 different phones and they will all produce the same codes at the same time.