Does the "trolley problem" have any validity or use?

I often come across people who think ethical philosophy consists of asking others what they would do in "hypothetical situations" in which they are allowed only two options, both terrible. One I keep coming across is that of the Trolley Problem proposed by Philippa Foot and modified by Judith Thomson, in which one must choose whether to kill one person or let five others die. Psychologists Jonathan Haidt and Joshua Greene even take fMRIs of people when they answer this question. Greene says that when someone chooses to sacrifice one individual, the prefrontal cortex -- which regulates impersonal, long-term decisions -- lights up. By contrast, when one refuses to sacrifice the individual, blood rushes to the amygdala -- the part of the brain regulating empathy and visceral emotional responses. Is it valid for moral philosophers to pose the Trolley Problem to people and to insist that people's answers show that one can only either be a deontologist or a utilitarian?