That stability claim is an average for all American households, gathering together high-income households and long-tenure homeowners along with poor renters. But in a K-shaped economy where the wealthy do well and the rest do worse, averaging the two forks of the K hides the hardship of those on the lower fork.
From https://www.jchs.harvard.edu/blog/rental-housing-unaffordabi...
> The net effect of this longer history is that renters today spend much more of their incomes on rent than they did in previous generations. The median renter household in 1960 spent less than a fifth of their income on rent. By 2022, housing costs consumed 31 percent of the median renter’s income. And in inflation-adjusted terms, the median rent is up 75 percent over these six decades while the median renter income has risen by just under 15 percent.