“Oh no. It is too tough,” locals told us.The Chinese military had cut a path up over several mountaintops, just in case the helicopters could not fly due to bad weather. We all agreed, if we could make it, the hike would be worth it. We loaded up our gear: equipment to broadcast live, some water and food.

http://inthefield.blogs.cnn.com/2008/06/01/the-trek-to-beichuans-quake-lake /

1. I know mountaintops and mountains are two different things. My question is why mountaintops is preferred over mountains?

2. Could you recommend a substitute for the bolded words?

Because the path goes over the tops of the mountains.
Having looked at the CNN report, I would leave the bolded words as they are. It is informally written and this phrase fits into the style.
goes over the tops

This totally makes sense. Thanks,Feebs.