Bitpay payment protocol

Many sites that claim to provide anonymous payment option now force users that wish to pay by bitcoin to use “BitPay”. In this case one must use Bitpay’s payment protocol and the payment address isn’t available.

My gut feeling says security / privacy / anonymity must suffer when they force one to use their protocol instead of just providing a bitcoin address.

Am I right?

Edit: I just found that:

I don’t need anyone to save me from “delayed transactions”. I can set the miner’s fee I like and if I set it too low and that means a delayed transaction so be it. You know what? maybe I don’t care about a fast transaction at all. And if I made a mistake because I’m stupid then I’m willing to suffer the consequences.