of course it sounds tempting and plausable, they are not going to say, "were ripping you off here" car dealers, estate agents, and bloody sales reps, are all the same
you are having doubts, and can see yourself its all suss, as you say, they know nothing about you, yet allready have a booking lined up, if they are serious, why not take you fee after the booking
Like my mother used to say, if it sounds to good to be true, it probably is, and thats definatley the case here, walk away keep your money, and hopefully you will find a legit agency soon