As a note tampons shouldn't be uncomfortable, if they are, you're using the wrong size or inserting them wrong. I've trained horses, been on a diving teams, played tennis, and never been "uncomfortable" with them... Use a pad if you don't like tampons. It's just not safe nor acceptable to be wandering around in public bleeding all over...
Sorry, I'd be just as... "disgusted" if someone left their nose bleed on a public surface (bench, table, w/e) so it has nothing to do with "women's natural" shit at all. It's not acceptable, sorry.
As a historical note, in the past women used a lot of things even grass and leaves; some women knitted pads that they'd wash daily/hourly, doubling up their knickers, hankies, etc. It was apparently traditionally seen as a woman not doing their "job" of making more kids if they menstruated so it is even suggested that women didn't menstruate as often as they do these days - and considering larger family sizes, the old tradition of marrying young, and dis-health (which can cause early menopause) I can see that reasoning. Many religions also have "guidelines" for a woman's menstruation, including the edict that they wear pads of some kind (wool, leather, etc.,) and even cloth self-made tampons (Jewish tradition) and I presume those rules are what was followed by the majority of women in the past. It was stated that in India, even today, the use of anything at all is considered taboo so they just "bleed freely" but I'm unable to confirm that on any second site.
All and all, given my quick read on the historical subject, I've come to the personal opinion that this woman's full of shit and just wanted attention. Women without money are not going without menstruation aids, they're simply making their own.