Umm, you definitely can explain your way on to a flight.
When a TSA agent asks if they can search your bag, saying "yes" has always lead to me catching my flight, and I'm pretty sure saying "Let me talk to my lawyer" would lead to me missing my flight. Also when they asked if there was any reason you might have set off the bomb detectors, answering with a valid reason can definitely lead to you catching your flight.
However, as soon as its clear you're going to miss your flight, I would agree its the time to stop talking.
When a TSA agent asks if they can search your bag, saying "yes" has always lead to me catching my flight, and I'm pretty sure saying "Let me talk to my lawyer" would lead to me missing my flight. Also when they asked if there was any reason you might have set off the bomb detectors, answering with a valid reason can definitely lead to you catching your flight.
However, as soon as its clear you're going to miss your flight, I would agree its the time to stop talking.