As a person who majored in Computer Information Systems but is considered a "business person" (ecommerce manager) I can confidently say that this problem does exist in the workplace by most "business people". It doesn't only happen at small/mid size companies. This problem exists even at the enterprise level. We are very highly ranked in the IR500. (top 100)

The way to overcome this problem is make very clear to executive "business people" how risky/costly (change management, bugs, etc.) a relatively small problem could create.

For example in ecommerce if you make a "minor" change to the checkout process which results in the site not accepting orders, or even a small percentage of orders the damages would be substantial at a financial, and customer level.