Can someone explain to me how this works legally? It seems a bit too convenient that you can ignore someone's T&Cs and use an unlicensed third-party service instead.
Google's cached Craigslist site is, legally, a copy of the Craiglist site, which just happens to be hosted on a different server with permission (under fair use, it is essentially compelled permission).
Craiglist does not own the facts on their website (nobody can own facts), but they do own the data (a filtered or specifically selected set of facts) or a license to use the data. They also have a license to post the listings (which are owned by their users). These licenses do not extend beyond Craiglist.
Craiglist's T&C bars scraping because that is an end-run around both the user's copyright in the listing and Craiglists' licenses in the listings and underlying data.
By scraping from a copy of Craiglist's website, 3Tap and Padmapper are still scraping from Craiglist's website.
2: The US Supreme Court has in fact decided that the 'data' is not not copyrightable in terms of phone book listings. Because they are no longer scraping off Craigslist itself, they are no longer violating terms of service directly. Craigslist doesn't get to control what Google or 3tap allows. See: http://news.ycombinator.com/item?id=4219085
2) You need to reread your SCOTUS case law. The specific selection, arrangement, and presentation of basic facts is copyrightable. This is why phonebooks and whitepages are copyrightable, even if the information they contain is not.
The key here is the selection of fields--is it sufficiently unique that it would not be the most efficient and obvious way to present such data? With a phone book, you have few fields: name, phone number, and possibly an address. There are only so many ways to select, arrange, and present such information.
With rental postings, there are many more fields. The selection of fields itself can be considered unique, as they tend to very from site to site; address is really the only constant. Consequently, the phone book cases are not strong protections for Padmapper and 3taps. Thus, if 3Taps' api makes available all of Craiglists' fields for copying, that will probably be enough for a violation of Craiglists' license.
http://www.bitlaw.com/copyright/database.html
http://www.bitlaw.com/source/cases/copyright/feist.html
If you read the second link, you'll see that it is exactly what the OP is doing and it has already been decided in favor of the database owner in case law.
Applying this example to the Craigslist situation (in a decidedly IANAL fashion), Craigslist would have to be able to argue that the manner in which it "selects", "coordinates" and "arranges" its data is creative and unique enough to be protected by copyright law, and furthermore that PadMapper's use of the data infringed on that specific creative selection, coordination, and arrangement of the data (since the data itself is still not protected by copyright).