Just be be clear, I am NOT a dreamhost employee. Just another customer that has been around awhile.
Dreamhost didn't choose to save a few bucks by not having phone in customer support, they created there business model around that fact. (BTW they do offer phone support, but they charge extra for that and you do have to be able to log into the panel to use it.)
Frankly I'm kinda glad that dreamhost doesn't choose to let the entire staff do account verifications. I'm personally happy that they relegate that task to a limited team that understands just how easy it is for a scam artist to confuse the situation.
How you can avoid the problem in the future is to have a non-dreamhost email account registered as a panel login. It's that simple. No need to wait for help from anyone.
One thing dreamhost could do a better job at tho is reminding you think thru your account access backup plan. When you originally sign up your panel login email address has to be a non-dreamhost email, because you have to receive the account setup email before you can set up your account. Somewhere in the workflow of changing that login email address to a dreamhost based email address there could be a warning that you may want to keep an outside address as backup, and as an alternate contact for support to use should your dreamhost email not be functioning for any reason. Seems like something like that could save the account verification team a few future headaches too.