It's true that lower income families spend a higher proportion of money on food [0], but that was equally true in 1963. It's a static fact about income brackets at any time, and doesn't explain the change in average share.
Food share dropped from ~30% to ~6% because real incomes have risen and food has become cheaper relative to housing, healthcare, education, and so on. That shift affects all income levels, including the poor. Your point doesn't contradict the article's, that the poverty line, based on 1960s food budgets, no longer reflect current costs of living.
Could you send the article where the author revises their claim?
In the 1950's poor people in America may have had housing, but there's a good chance that housing didn't have plumbing. Poor people in the 50's spent roughly 0% of their income on childcare. Much of the article is complaining about the cost of child care.
You may think that poor people should be able to afford child care. That's a valid thought. But then you can't compare that to a 1950's definition of poverty where child care is definitely not affordable by the poor.
In the 60s (and 50s, though not sure why we're moving backwards) most households were single income; childcare costs were virtually nonexistent because mothers typically stayed at home to raise children, and a family would get by on the father's income alone.
That actually illustrates the point nicely: typical economic and living situations from when the metric was created were very different from today in a variety of ways, and once again, the reason the 3x food costs number was chosen -- that roughly 1/3 of income of low-income households was spent on food -- is simply no longer true.
Now, what the poverty line should be is a whole 'nother topic -- for the record the ~150k number is more as an demonstration of how broken the metric is than an actual suggestion, at least as I see it. This discussion doesn't seem to be going anywhere though so I'm tapping out, but I would still appreciate it if you would link to the article you mentioned.
The main reason the share went from 30% to 6% is because people are richer. Poor people spend more money on food than rich people.