I started out without shampoo about 20 years ago after reading a reference, just water and a vigorous scalp rub. My wife thought it was fine though I don't have long hair. And it seems absurd to put detergent in your hair followed by an additional product just to put back the oils removed by the detergent.
As a regular gym goer, what smells is /bacteria/. Fresh sweat doesn't smell bad, old sweat does. Same thing goes for urine.
Wash your body and clothes regularly, you don't need deodorant and it won't save you if you haven't washed your body and clothes.
Underarm BO is a totally separate thing, and he's right that most all koreans and east asians don't need to worry about the bacteria that causes that particular smell.
If you go to korea, you'd have a hard time even finding a place that sells deodorant.
So your old coworker is either in a very small minority group, or just had other hygiene problems that are not specifically underarm BO.
I have worked for almost 20 years and over that time I met only one individual who had "issues". Most people try their best to look and smell as good as possible.
Mind you, they're not always the best put together folks -- flabby 30 something dudes in ill-fitting shirts and cargo shorts, yes cargo shorts in 2019 -- but most of em clearly had a shower recently and brushed their teeth.
That's just unnecessary.
I'm not trying to win a fashion show at work while sitting in my office not talking to clients. I'm wearing clothing that's functional and comfortable. Only random people on the internet seems to actually care about this, and can never seem to explain why they care so much. It usually comes down to some spurious nonsense about "neckbeards."
I learned about the effect of eggs when I tried a high protein, low carb diet where I ate 2 fried or scrambled eggs every morning. Within 3 days of starting the diet I developed an unpleasant fishy body odor, especially in my armpits. Normally I would eat 2 eggs once a week, at which level I did not develop the fishy smell. Even washing my armpits with soap did not eliminate the odor. I stopped eating eggs daily and within a couple of days the odor cleared again.
Similarly, I do a 10-12 day self supported pack hike most years. For lunch on these hikes I typically eat some form of processed meat (cacciatore sausage, salami etc) with processed cheese and dry biscuits. On these hikes I can usually swim or bathe in fresh water a few times each day without using any soap. I notice a slow increase in body odor, again mostly from my armpits over the course of the hike. I suspect the body odor may be caused by the garlic from the sausage. The other foods I eat are things I eat regularly without issue. Unlike with the eggs, this odor goes away with the first hot, soapy shower when I get back to civilisation.
Note that in the past I have had girlfriends comment that I had very low body odor compared to other guys they had dated.
So I suspect that successfully switching to a no or very low soap hygiene routine might be challenging for people whose diet and genetics mean they excrete odorous, non-water soluble compounds.
When I tell hairstylists, the reaction is shock/disgust followed by surprise when they can't help but do the smell test, and it doesn't smell, and then with the unprompted admission that I have "abnormally" thick and healthy hair.
I also just use unscented, clear, vegan, glycerin soap on the important bits, but I'm going to experiment with stopping that after reading this article.
Apparently, when switching to natural deodorant it's supposed to get worse before it gets better which didn't happen for me.
I've asked my partner who has a pretty sharp nose and she agrees with me.