Your Life or a Black Hat During Davening

Between Minchah and Ma'ariv this evening, I spoke about the prohibition of writing on chol hamoed, and the tension between the prohibition of writing as stated in the Shulchan Aruch and our general laxity regarding the prohibition. After all, if I feel the need to write for practically any reason, one can easily justify that need as either צורך -- a necessity for the chag, or מעשה הדיוט - the act of a layperson -- or both.
In any case, after Ma'ariv a wonderful young teacher in the community approached to briefly discuss the topic. "I was sitting outside my house today working on my classwork," he told me, "and I wondered whether I should perhaps not be writing in such a public manner. While I know that I'm writing limudei kodesh, my students might not, and they might think that one is permitted to write anything on Chol Hamoed."
I agreed with him, and we walked out of shul together. As we left we realized that both of us had ridden our bikes to shul for davening. (With gas prices skyrocketing out of control, every little bit helps.) The only difference between us was that I was wearing a helmet, while he was not.
I let him have it - the poor guy. (Unbeknownst to him, helmet-wearing is a particular pet-peeve of mine, and I have spoken about it from the amud in shul on a number of occasions. For a number of years I as I drove around the community I would randomly hand out coupons for free Slurpees to kids who wore their bike helmets -- until 7-11 stopped sending us the free tickets.)
"How can you ride your bike without wearing a helmet?" I attacked.
First he tried explaining that he only rode on the sidewalk, so he didn't need one. I'm not sure where he got that idea from, as one can clearly reach dangerous speeds riding on a sidewalk, and even at slow speeds suffer severe head trauma from a bicycle spill.
His real answer was simple - and obvious from the hat on his head. He needed to wear a hat during davening, and there was no way to ride the bike with a helmet and also bring the hat. He feared that his students might see him davening in shul and think that he only wore his hat in school, and not at other times. So he chose the bike over the hat.
And what example, I asked him, does this set for your students about wearing a helmet when they ride their bikes? Do they know that you're only riding on the sidewalk? If you're concerned about maris ayin on the possible d'rabbanan of writing on chol hamoed, shouldn't you be far more concerned about maris ayin on sakanas nefashos?
In truth, I don't want to seem overly critical of this rebbe, who I love and respect very much. I just wonder how wearing a black hat during davening can become a greater concern than wearing a bicycle helmet. Am I overreacting? Is it just because I don't wear a hat -- so I don't understand?