Do flight recorders float in water?
You are correct in the assumption that the typical data recorders being used today are too heavy to float.   They are designed to withstand very high forces, extreme temperatures, and to withstand corrosive environments (like sea water) for long periods of time. 

For example:


  A DFDR must obviously have a high degree of ‘crashworthiness.’ The
  first units were required to withstand a momentary shock force of
  1,000gs, the latest test standards now call for a test to 3,400gs for
  a duration of 6.5 milliseconds. The units also have to withstand a
  static crushing force at all of its six axis points of an applied load
  force of 5,000lbs for 5 minutes on each axis. Third, it must withstand
  a 500lbs piercing force test conducted by dropping it onto a ¼ inch
  steel pin from 10 feet. Lastly it must withstand a 1,100°C fire test
  for 60 minutes, and a 260°C oven test for 10 hours. 
  
  It is also required that these units are mounted within the tail area
  of an aircraft, away from the potential crushing force of any engines
  mounted nearby. The DFDR must be watertight to a depth of 20,000 feet
  in sea water, and survive at this depth for 30 days - and it must be
  fitted with an underwater locator beacon which will act like a sonar
  transmitter, by ‘pinging’ a signal through the medium of water that it
  might be laying in.


Time has an article showing the Air France 447 flight data recorders resting on the bottom of the ocean (there are others there):

  

This particular FDR is pretty common, and weighs about 13.5 pounds1.

Without seeing the original interview, I suspect that the author of the article got confused during the interview and was told that radar could detect debris the size of a soccer ball that is floating in the water and at a different time mentioned that they would be looking for the radio signals emitted by the black box (which wouldn't even be detected by radar).



UPDATE:

That being said, there are black boxes that can float and even eject from the airplane when a crash is detected.  They seem to be more common in military aircraft, and there have been a few attempts to require them in the US (and even have the government pay the $60,000/airplane price) but the bills stalled in congress.  The lawmakers here have recently started discussing this again though.

Deployable Black Boxes have been around since the 60's and are a second set of black boxes meant to be a backup to the main ones.  They can be particularly useful when crashing into water or in the event of a major fire because they would not be within the main crash site.



Here are a couple of articles about them:


Lawmaker Calls for 'Black Boxes' that Eject from Planes
Canada’s ‘deployable recorder’ would have located missing airliner within minutes, experts say




1 See specifications on Honeywell's webpage and page 7 of their product description.