Looking for alien life on Earth.

Here's a NYT op-ed (about why we should search Earth, not Mars, to find alien life forms) that brings up a question I've been meaning to look for answer to for a long time: why isn't it inconsistent to believe that all the life we know on Earth traces back to a single cell and that other planets that have Earth-like conditions would give rise to life? It seems to me, that if Earth-like conditions get some life-creating cell started, that there should have been many such cells on Earth, starting many different evolutionary lines. Even if in the end, one line became so successful that it rendered the other lines extinct, wouldn't there have been a period in which multiple lines coexisted?

From the op-ed (by astrobiologist Paul Davis):

Genetic sequencing is used to position unknown microbes on the tree of life, but this technique employs known biochemistry. It wouldn't work for organisms on a different tree using different biochemical machinery. If such organisms exist, they would be eliminated from the analysis and ignored. Our planet could be seething with alien bugs without anyone suspecting it.

How could we go about identifying "life as we don't know it"? One idea is to look in exotic environments. The range of conditions in which life can thrive has been enormously extended in recent years, with the discovery of microbes dwelling near scalding volcanic vents, in radioactive pools and in pitch darkness far underground. Yet there will be limits beyond which our form of life cannot survive; for example, temperatures above about 270 degrees Fahrenheit. If anything is found living in even harsher environments, we could scrutinize its innards to see whether what makes it tick is so novel that it cannot have evolved from known life.