No, the air isn't so thin above 10,000 feet that a match won't light. On the other hand, the butane in your lighter might not spark in freezing conditions. The same problem plagues the lightweight, quiet, efficient canister camp stoves beloved by sea level camping enthusiasts.
Liquid and multi-fuel stoves are a better choice for high altitude camping. However, they do have their drawbacks. They require priming, are heavier than canister stoves, and emit a loud "jet engine" sound that may interfere with the Zen of camping at high altitude.
You can sometimes eschew a camp stove and light an old-fashioned camp fire for cooking. However, because of the scarcity of wood above the tree line, fires are often banned in higher elevation camp sites, making a good high-elevation camp stove a necessity. Whether you cook over a stove or an open fire, you'll need to allow extra cooking time at altitude since decreased air pressure means that water takes longer to boil and food requires more time to heat through.
Also keep in mind that, once consumed, food will eventually pass through your system and out the other end. Is it really true that you have to pack your own privy when you're camping at high altitudes? Find out next.