As with many situations in flying, "it depends"... Overall, though, I agree with your first instructor.
First, it depends on airplane performance. In a light single-engine airplane, there is little difference in stall speed with flaps up or down. Also we almost always fly the landing pattern above flaps-up stall speed, even when the flaps are down. When you aare able to safely raise the flaps without having to dive to gain airspeed, raising them is a good idea when you are at higher altitude (above ~500', depending on conditions). After you establish your flaps-up glide, assess the situation and lower them as drag is needed to make the runway.
Your second instructor gave you a couple examples of techniques that may be used by experienced pilots in extremis. The "dive below airport altitude" situation depends on having enough airspeed, the flight characteristics of the airplane when flaps are extended, and assessing potential ground effect advantages. Similar stories about "jumping" fences abound. However, if you happen to be flying an airplane that does not "balloon" when flaps are initially lowered, the technique may not work, and you need to be VERY aware od airspeed.
The bottom line is that best STABLE glide is with flaps up, though you may use some short-lived tranisent effects to your advantage.