Some readers may fail to actually read the assignment. But whether you read exactly what the assignment requests or not, the parent is right in his statement that the problem used an overly complex method to teach students.
I had never even heard of a "number line" until a saw the problem shown in your link. After taking a moment, I can see how it could be used to determine an answer. However it is overly complex and takes the students in a direction that shouldn't be used because number lines cannot be used when the student moves beyond basic arithmetic. While the assignment wasn't to create a number line, it was still asking a student to realize what was incorrect with one that was given to them. This means actual students are taught to use number lines when solving basic arithmetic problems, like 427- 316 = 111. Basic arithmetic is a foundation and can typically be carried out in a very simple manner by writing one number over the other and performing the correct action on each column of digits. It is simple and can be used in their future endeavors and studies. Drawing lines with many nodes for 1's, 10's, and 100's cannot be used beyond basic arithmetic problems. Why confuse the students by adding an overly complex method of doing things when they can be taught to write two numbers and calculated the difference in a simple and easy to understand manner?
Second, when children are young and still learning a concept, they should not be shown problems that are incorrect when learning about the concept. Searching for an error and explaining it may allow a person's understanding of a topic to grow if they already understand the subject matter. However, when students are still learning the basic principles of something, they should not be shown incorrect ways of doing things. Lets say a child knows that a problem has one flaw in it, but everything else in the problem is right... just like in this homework assignment. If the child is incorrect in determining which part is flawed and which parts are correct, then the problem could actually reinforce the incorrect way of doing things.
The parent was correct in his rant. If the assignment insists on having a student determine what "Jack" did wrong when solving a math problem with an overly complex method, then the answer is that Jack should just subtract 316 from 427 and should not draw a diagram .