Document check may come after or during eligibility check, and medical request comes after eligibility. And yes, eligibility does not just mean the number of points you have, but also settlement funds.
The way I see it based on what I can glean from my CAIPS notes: they awarded me more than 67 points, then they asked me for proof of funds and police certificates. Once they are happy with my proof of funds, they issued medical (about 10 days after I submitted my bank statements), but BEFORE they evaluated my PCC (since I submitted my PCC just 1 day before I got medical).
Medical request seems to be issued after eligibility (number of points AND POF) is passed, but not necessarily after criminality (rgb got his medical request only 1 day after getting a request for PCC), though it does look like they're also waiting until after RCMP screening is over too (Shomo got stuck here).
There have been cases where rejection occurred AFTER document request due to number of points (immc and andy.fan), but it's because they were not awarded adaptability points. So the process, based on what I can observe so far, goes as follows:
1. Ottawa visa officer checks your work experience letters, then evaluate your number of points (maybe taking for granted what Sydney had for adaptability)
2. Issues POF and PCC requests
3. After getting POF, he checks again for number of points, this time, verifying adaptability into more scrutiny
4. Issues medical request (PCC usually may or may not be received yet at this point)
5. Third line on eCas showed up (once medical and criminality are passed)
6. Begin security check (this could be short or long, depending on a lot of factors)
I think, if you do not claim and rely on any adaptability points, and you already got document request, most likely they have passed you on selection factor. This is the case, I think, only for January 2012 to April 2012 applications, whereas some latter applications seem to have been evaluated much faster, and I'm not sure if the same assumption can be made to these ones.