Pros:
* You'll be working with them rather than against them.
* Your solution will be far more robust.
* It'll be way cheaper, supposing you account for the ongoing maintenance costs of your fragile scraper.
* You're eliminating the possibility that you'll have to deal with legal antagonism
* Good anti-scraper defenses are far more sophisticated than what the author dealt with. As a trivial example: he didn't even verify that he was following links that would be visible!
Cons:
* Possible that target-site.com's owners will tell you to get lost, or they are simply unreachable.
* Your competitors will gain access to the API methods you funded, perhaps giving them insight into why that data is valuable.
Alternative better solution for small one-off data collection needs: contract a low-income person to just manually download the data you need with a normal web browser. Provide a JS bookmarklet to speed their process if the data set is a bit too big for that.