Authorize.net is telling my client this, what does it mean?

I just got this from a client. Anyone know what it means or what I should do?

"I am also having a serious issue that was brought to my attention today. Basically the website is processing orders that have been declined. For instance I have a customer (Jane Doe) who made a purchase and my fraud filters did not process the order because the zip code provided was incorrect, but the bank released funds because the funds where available. So in short the order showed up in ZEN CART which is not suppose to happen, but was declined in Authorize.net. I was unaware of this issue, but the girl who process' orders in the shop informed me this is actually happening on a few occasions. The Rep. from authorize advised that I tell you the following:

It's better to test for the response code, rather than testing for a authorization code. Because the response code is more accurate.

He mentioned is was a easy fix, (I have no idea how to though). Please advise if you will be able to fix this issue as soon as possible."

This shop is running Zen V 1.3.5

Zen Cart does test for the response code. It would only accept the order if the response code coming back from the gateway was an approval, as evidenced by the bank releasing the funds.
It does not deal with AVS responses. If you want a certain AVS response to prevent acceptance of an order, you'll have to work with your Authnet rep to set up the rules in your authnet profile to cause a decline if there is an AVS failure.