I used to work with a very wise man who says this all the time. I think it was his way of making it OK to do something that you didn’t think was the right way, or the best way, or the most elegant way because the client asked for it. It was also his way to help new people at our agency understand that just because they have responsibility for a certain area of a project doesn’t mean they’re 100% in charge. After all, it isn’t YOUR project it is the CLIENT’s project. The client is paying you to do certain work. It needs to meet their goals and needs and preferences in the end, not yours. So ultimately it is not your decision, it’s theirs.
There may be times when what the client is asking you to do is not actually a matter of opinion. What she’s asking for is actually detrimental to the project. If this is the case, it is sort of your job as the project team to discuss it. A good rule of thumb is to bring it up, explain the reason why you think it could be detrimental to the project, and make a suggestion for how you might accomplish the same goal without risking the end result. This strategy works best when the core team member responsible for that area of the project (e.g., programmers for coding issues, graphics people for art issues) is the one making the argument – assuming of course that those team members have great communication skills and are putting the client’s best interest first (rather than trying to get out of doing more work themselves).
If the client disagrees and repeats that she wants it her way, then you do it. Because its her project, not yours.