Healthcare costs more for obese people...thats why so many work places offer free gym memberships.  I'd bet that this is as much a $$$ issue as a fit for duty issue..

If you have a desk job, do you still have to pass the fitness test?

Yes.  All members of the Army regardless of job have to pass the same physical fitness test and the same height/weight requirements.  There used to be more leniency given to harder to recruit jobs like doctors and lawyers, but that is going away with the draw down and the fiscal cliff.

Active duty Army is required to take and pass the APFT 2X a year.  Army Reserves is required to take this same test 2X a year as well, Army National Guard is required to take the APFT just once per year.  And no I have no idea why the 3 parts of the Army differ on this.

In addition all Soldiers are required by AR 600-9 to maintain weight or body fat.  The Army has max weight standards based on height and age for what is allowed as a maximum weight.  Failure to make weight standards is not a show stopper though.  If you don't make the table weight then you will get taped for body fat percentage.  If you pass the body fat standard then you are in compliance with the regulation.

Now admittedly the Army does have some broken Soldiers that cannot take certain parts of the APFT.  The test is 2 minutes of pushups, 2 minutes of situps, and a 2 mile run.  Broken Soldiers can get a profile that will exempt them from certain parts of the test.  A common profile is for the run portion and an alternative test is given in its place.  The most common alternative test is the 2.5 mile walk.  Those that I knew in the service before I retired said the walk was no walk in the park and said passing the run if they could run would have been easier than passing the 2.5 mile walk.  BUT even though the Army has broken Soldiers I have never heard of a waiver against passing weight or body fat standards.

As to the statements about not tossing an overweight doctor or lawyer in the Army well that just isn't so per the regulations.  Lawyers and doctors are made officers in the Army because of their position and as such are in positions of leadership.  The Army is very muych into the concept of lead by example.  Officers and NCOs, regardless of position in the Army get held to a higher standard.  Private Joe Snuffy cannot be expected to perform his duties and comply with Army regulations if his superiors are not held to the same standard.

Failure to pass the PT test or make weight does not lead to an automatic discharge from the Army.  There is a process in place where if you fail the PT test you will be retested in X number of days and not until after the 2nd official PT test will they start the seperation process.  Same with weight control.  Failure to make weight or body fat will get you into the weight control program and the first stop to that will be a trip to the doc to evaluate your weight and determin if its Cheeto's or medical related for your fatness.  You are then placed in the weight control program and monitored monthly.  You MUST make forward progress each month or face discharge, you also have to make body fat % by a certain date as well.  Can't remember if its 6 or 12 months to get off the program.

As to the article and just now discharging Soldiers for weight related issues.  Well that part is just utter total BS.  I enlisted back in 1987 and the program was in place long before then.  It is not JUST happening now.  The article is getting the light of day now mostly because the writer was likely bored and needed a news article to print.  But I will say the Army is tightening the books on its service members.  Last year the Army declared itself 50,000 over strength and over the next 5 years (4 now) it would shed 10,000 a year mostly through natural attrition.