He made that assumption because it happens by default. Once a monkey makes an error in Hamlet's first sentence, the data stream for the full sentence starts over. The monkey really just represents randomness. Once you find that one part of your random string of output doesn't match your first sentence, you re-start looking for that sentence again in the output. That's the same as saying that the monkey starts over. The monkey isn't really starting over, of course, it's just banging away on the keyboard, but we start over in the sense that we re-start looking for a match again in the monkey's output as soon as we find the first error.
This applies to the data stored in DNA just as easily as it does to the data stored in Hamlet. As soon as you see that the random sequence no longer matches your search pattern, you re-start at that point looking for a match on the first data byte.