Your instinct on the exposure is correct. When a VA calls in your name, any fair housing or TCPA/DNC violation complaint names you first, not the agency. The agency's general liability policy, assuming it exists and covers professional conduct, does not protect you from regulatory action. That is a separate question from insurance entirely, and it is the one neither rep could answer because they probably have not thought about it.
The certificate with a policy number and no limit listed is effectively useless as due diligence. A valid certificate of insurance shows the policy type, the carrier, the coverage limit, the effective and expiration dates, and you as an additional insured if you are requesting that status. Anything short of that is paper for the file, not actual coverage confirmation. Ask them to reissue it through their broker with your entity named as additional insured on the general liability line, and see how they respond. That request alone tells you a lot about how operationally serious the agency is.
On E&O specifically: most VA agencies do not carry professional liability (E&O), and the ones that do rarely extend it to individual client relationships the way a law firm or title company would. Confirm what is actually on that policy and what it covers. A licensed insurance professional can read that certificate in about five minutes and tell you whether the coverage is real. That is the right person for that question, not the agency rep.
The compliance risk you named, fair housing complaints and DNC violations tied to calls made in your name, sits with your business regardless of what the agency carries. That is a legal question your real estate attorney should address before you sign a service agreement, specifically around indemnification language and what happens when a call made by the VA generates a complaint.
At $1,100 and $1,400 a month, what does the service agreement say about indemnification if a compliance violation occurs during their outreach?