The only correction is that you have to do BOTH. It's not enough to carry all the flat repair stuff, OR have new tires sitting on the shelf ready to go.
I recently got 2 flats. I carry 2 tubes, patch kit, boot, 2 CO2's and a mini-pump. But my Vittoria's are getting worn and most importantly - I DO NOT HAVE NEW SPARE TIRES SITTING ON A SHELF OR INSIDE A DRAWER.
Thus my first 2 flats in 2 years.
SB