Actually, a good commercial printer is going to be way more than 300 DPI (The Epson R300 prints at up to 5760 x 1440 DPI).
An HD capture is going to be, at best 1920 X 1080 – Roughly equivalent of a 2 megapixel photo, which should not be used for printing more than a 4″ X 5″ photo with any hopes of a decent product.
