That's a bit hair splitting but, for me parsing is more about reconstructing the structure from a flattened representation. I even dig a supporting online definition: parse:

1. To determine the syntactic structure of a sentence or other utterance

And here he does not need to think about the structure - all he needs is that the needed information is just after and just before some specified strings.

Following the structure of the document is usually more general way of searching the needed information, because it is more formally defined, but sometimes you don't need to do that since you know about other properties of the data that can lead you to your goal (and sometimes you don't know much about the structure of the document).