Yeah, that's pretty much how I "summarize" things, too.

Take part "X" and "Y" from the page, reword said parts to my liking, re-reword said parts in a way that it reads in a smooth and coherent manner.

I usually read the part I'm going to summarize first as a normal read-through, afterwards I'll go back and start re-reading that part of the book and start summarizing. It's a great way of rehearsal.