Guilt for Excercise? A Torah Value Taken to the Extreme

My weight and I have long engaged in a friendly, and sometimes not-so-friendly competition. It tries to the get the best of me while I struggle to keep it under control. I was never one of those people who could eat whatever I wanted and maintain a healthy weight (and found myself quite envious of those who were). For many years I adhered to a SugarBusters diet (though I fell off that wagon about a year ago), and since my college days I've been a regular runner. (Back in semichah, when I lived in Washington Heights, I used to run over the George Washington Bridge. It was a great, beautiful run.)
Aside from the issue of trying to stay healthy, I just feel better when I excercise, both physically and emotionally. Running helps me stay calmer, more balanced, and well-adjusted. I figured it was a good thing all around.
Then I received the OU's most recent Shabbat Shalom email, which contained an article entitled, "Why Do I Feel Guilty When I Run?" in which Rabbi Pesach Sommer, who lost about 100 pounds over the last year writes,

So when I began to vigorously engage in what seemed like a strictly physical pursuit, I felt guilty. I was uncomfortable with activities like sports and exercise. Running, with all the health benefits it had to offer, left me uneasy.
I tried to ignore the little voice in my head that told me that running was bitul zman, a waste of time. When that didn’t work, I tried to convince myself that my time in the gym was justified by the fact that it would allow me to live longer and fulfill the goal of v’nishmartem meod, protecting my life. I suppose that should have been enough, but somehow it left me less than satisfied. Not enough to get me to stop, but, still, I was determined to understand and hopefully get rid of the gnawing feeling I was experiencing.

Rabbi Summer ends his brief article concluding that his excercise was actually improving his spirituality, which is nice and true. But reading the article, I found myself wondering, "Why in the world did he feel guilty? What if he achieved no spiritual nirvana through running, but simply led a more healthy lifestyle? Where did we get the notion that excercise is "bittul zman"?
A commenter on the article states it this way,

I'm actually shocked and even horrified at the idea that we Jews have produced a culture that could leave someone feeling guilty for exercising.

I believe that the answer - and the source of Rabbi Sommer's guilt - lies in a good value taken to the extreme, which manifests itself in many areas of Orthodox life.
Judaism considers the study of Torah to be a core component of a religious, spritual life. In fact, halachah considers Torah study to be obligatory. One must study Torah. The question is: how much? For how long?
Boiling a complicated halachic discussion into a nutshell, two basic opinions emerge. The first, articulated by Rambam and actually encoded into the Shulchan Aruch (Yoreh Deah, 246:1), posits that one must, at a minimum, study Torah every day and night. They derive this from the verse where God tells Yehoshua, והגית בו יומם וליליה - "and you shall delve [Torah] day and night." (Yehoshua, 1:8) According to the most lenient position, one can even fulfill this obligation with the simple recitation of the Shema each morning and night.
On the other side of the spectrum - way, way on the other side - is a chorus of opinions that take the verse quite literally: one must study Torah at all times, always, day and night. According to opinions in the Talmud, this precludes any secular study (See Menachot 99b), learning a trade, (See Mishnah Kiddushin 4:14), and basically anything else. Any activity, other than the study of Torah, is a waste of time, and represents the shirking of one's spiritual obligation to study Torah.
Despite the fact that the Shulchan Aruch ruled leniently, the strict opinion - perhaps even the most extreme formulation of that opinion, has become the guiding mantra of the entire yeshiva world. Any serious yeshiva considers, as one of its founding principles, that the study of Torah is not only the most valuable endeavor in which a person can engage, but that as a direct result, any other endeavor is, by definition, a waste of time, and must be calculated as such.
Is it wrong to have such an attitude? Of course it's not wrong. But I don't think that it's right for everyone. In fact, it might only be the correct attitude for a very small subset of people who are capable of devoting every waking moment to Torah study. For them, the sense of obligation to learn all the time propels them forward, spurring them to achieve greatness in their learning. But what about for everyone else?
How would you feel if you were told, from the moment that you walked into school, that you must study Torah without pause for the rest of your life...and if you just couldn't do it, either because while you liked learning, the hours of sitting were just too long; or you weren't all that good at it; or you needed to get a job to support your family; Or you were 100 pounds overweight?
I can tell you how you'd feel, because I've felt it: You'd feel guilty. You'd feel like you were wasting your time. You'd feel that running, to stay in shape and be healthier, simply couldn't be justified, no matter how unhealthy you'd become. And that guilt is not a healthy thing.
More importantly perhaps, this guilt-fest does not accurately represent the only perspective on this issue. The Torah also conveys other values that Torah Jews must consider. Case in point: living a healthy lifestyle. It's not simply a matter of common sense. Rather, being healthy is a Torah value as well.
Rabbi Shlomo Ganzfried, in his "Kitzur Shulchan Aruch (Chapter 32) writes,

הואיל והיות הגוף בריא ושלם, מדרכי השם הוא, אי אפשר שיבין או ידע דבר מידיעת הבורא והוא חולה, לפיכך צריך האדם להרחיק את עצמו מדברים המאבדין את הגוף, ולהנהיג את עצמו בדברים המברין והמחלימים את הגוף, וכן הוא אומר ונשמרתם מאד לנפשותיכם. 

Since it is among the ways of God to have a whole and healthy body, and it is impossible for a person to have knowledge of God when he is sick, for this reason, a person must distance himself from things that destroy the body, and purport himself in ways that bring health and well-being tot he body, as it is written, "And you will carefully guard your lives."

They don't emphasize that halachah in yeshiva, because if they did, every bachur would take a couple of hours, a few times of week, to get some excercise. And he'd do it, not because he was overweight, and not because he couldn't feel his legs after hours of sitting in the Beit Midrash.
No, he'd do it because he saw his Rosh Yeshiva exercising too. And then, I am certain that he'd have no problem exercising without ever feeling guilty.