Let's do a back-of-the-envelope check: Let's estimate solar irradiance at best about 1 kW per square meter. Small high-efficiency panels convert about 20% of that to electricity, or about 200 W/m². 12 W / 200 W × 1 m² = 0.06 m² = 600 cm² ≃ 93 in², i.e. you need a panel with a surface area of 600 cm² or 93 sq-in to produce 12 W. That is a circular panel with a diameter of about 28 cm or 11" directed towards the sun. As an annular ring with a 20cm/8" hole in the center, it'd have a diameter of at least 50cm. The article states diameters between 56 and 61 cm (22" to 24"), so it seems plausible.
However, that size brim reminds me of a sombrero or an umbrella.
Gimmick caps with tiny fans and palm-sized panels have existed for at least three decades, though.