Decision trees are based on the assumption that you are indifferent to risk. This assumption is probably true if the amount of money at risk is substantially smaller that the total amount of money available. For large sums, however, the risk component can become important.
Consider the following example:
A simple decision tree analysis shows you that Option 1 has a higher expected value than Option 2. So you should choose Option 1, right? Well, not many people would be willing to risk losing $100,000 to gain $1 in expected value. Option 1 is significantly more risky that Option 2.
You might be tempted to argue that decision trees are fundamentally flawed. Rest assured that they are not. What is flawed is the notion that your first dollar is worth the same amount as your millionth dollar. This flaw is handled using a concept often referred to as utility.