OK, this is gonna be long, but I'd like to clear up a little terminology that the author of the article seems to have misinterpreted as well as the muscle-weight gain misconceptions...

First, about the article...
-Specificity: There is an Astrand citation that is grossly misinterpreted by both individuals in the article. When he speaks of "specificity" of training, he is referring to biomechanical specificity. This means that you analyse the activity which you desire to improve for things like muscle groups involved, joint angles, and movement velocity, and you attempt to base your strength program off of these variables. What specificity does NOT mean is that you should ONLY train the specific activity you wish to improve, or that you should modify that activity in an attempt to build "specific" strength"

-Mr. Stern also cites a Jones and Carter article that refers to the "4 key parameters of aerobic fitness." He interprets the parameters as not being affected by strength training. On the contrary, exercise economy is shown by countless peer-reviewed sources to improve with strength training.(Exercise economy being the body's ability to move itsself efficiently) This involves extensive neurological changes in how the brain is able to signal the motor units in the muscle to contract.

Muscle-weight gain...
Weight gain as a result of strength training would only be a concern in males (and the VERY VERY rare female) that gain large amounts of muscle mass in response to ANY weight training regimen. Women don't have enough testosterone to gain more than a few pounds of muscle in response to the type of weight training program that would assist in cycling.
Also, Muscle growth is seen almost exclusively in Type II (aka Fast Twitch) muscle fibers. An elite cyclist is where he (or she) is, in part, because of the large number of Type I (Slow Twitch) muscle fibers he/she was born with. What does this mean? No matter how much a person lifts, if they don't have many Type II fibers, they aren't getting any bigger! Stronger, yes, bigger, NO.
Strength is just as much (if not more) a result of neurological changes between the brain & muscle. Here's where I'm about to get everybody... the best training for these neurological changes is with high-load training in combination with high-speed training.
If you look at the strongest drug-free people in the world- Olympic Weightlifters- you'll notice that they aren't really that big- especially the women! Their training programs are almost exclusively low reps/high weight as well as low, but very fast reps with light weight. Now, take a look at the biggest people in the world- Bodybuilders- These guys live for muscle mass. They abide by high rep workouts... sometimes going as high as 30 or 40 reps.

So what does all this mean?
1. Strength training specificity for cycling would encompass things like parallel-depth front squats and back squats, step ups, good mornings, and ab exercises such as weighted situps.
2. Low repetitions of BOTH high speed and high load training are important to gain strength without size. Your program should include low-load exercises in which the concentric phase is performed as fast as possible (in speed squats, for example, you'd lower yourself at a "normal" rate, but raise the weight quickly), as well as high-weight exercises (enough weight to bring you close to failure in those few repetitions).

Hopefully noone fell asleep reading this. Maybe someone even learned something!