Smart skins are at least 20 years old and, like fusion energy, just around the corner since then. The usual concept is to embed optical fibers in the structure and shine laser pulses through them. If the fiber is damaged, it will transmit less light, and by measuring the return time of a very short laser pulse, even the location of the damage can be detected. This concept requires fibers with the same break elongation as the load-carrying material, so they break just when a crack in the structure starts. To detect even small cracks, a lot of fibers must be evenly placed, which is only possible with fiber reinforced plastics. The effort to place a light source and a detector at each end of every fiber has so far prevented a practical application, at least to my knowledge.
Other techniques send clearly defined "pings" through the material and detect the propagation of the sound wave with a number of microphones. By comparing the measured signal with a reference signal, damage can be detected in metal structures as well. This technique needs some processing power, but is easily within the scope of modern microcontrollers. However, outside noise will interfere with the measurement, so it needs well defined conditions to be effective.
The downside would be more mass, investment and operator training. Generally, more advanced techniques for structural health checks have been steadily introduced in the last 80 years. Given the high cost of maintenance today, I expect that deployed damage detection technology will continue to advance, with a healthy time gap to what is possible in the laboratory. So there is some truth to those BAe claims, but I would hardly call it revolutionary.
Even more advanced are concepts of self-healing structures which contain capsules of a two-component resin. When the structure breaks, the capsules break as well and the freed resin helps to mend the crack.
If you ask me, the mass of those microcapsules would be better invested if it carries load right from the start, so the structure will tolerate higher loads and more load cycles. But I guess those research grants need to be spent somehow, and marketing departments need to write about revolutionary discoveries on a regular basis.