The largest chunk of federal "cash transfers" is not welfare; it is retirement and disability spending. The rural population is significantly older than the urban population.
Bear in mind that rural poverty rates (~17%) remain persistently higher than urban poverty rates (~12%).
And in a high-wage urban area (e.g., Seattle), a $20,000 Social Security check is a tiny fraction of the local per capita income. In a rural area, that same $20k check represents a much larger slice of the total economic pie. This makes the reliance on government cash appear massive -- ~29% rural and ~17% urban -- even if the absolute dollar difference is more modest.
Also, metro areas receive MASSIVE amounts of federal contracting money (defense, science, universities, federal employees), whereas rural areas get virtually none.
Mostly this is caused by the "graying" of rural America and the persistent lack of high-wage employment in rural areas.