No, the SSN is on the tax return or form, still highly insecure. The data associated with the SSN in the IRS DB is linked to the hashed SSN.
So unless someone actually has the tax form (trivial for a few forms, difficult for massive amounts of forms) they cannot associate you with your SSN or your tax data. A corrupt IRS employee (and there are many) can easily enter one SSN into their application and get all your tax & income data. But they can't download EVERYONE's data easily.
We're talking about remedies to large data breaches here, not single experiences. Yes, your data is at risk while your tax form is in the mail or in the hands of an IRS employee, but as soon as it goes into the DB the associative data should be hashed. You don't eliminate breaches this way, you make them easier to deal with.