That's a dubious conclusion. Was there any hypothesis testing in this research, or just a graph?

Alternatively, by providing households with a consumption floor during times of temporary unemployment spells or subsidizing medical care when the household experiences a health shock, governmental welfare policies could reduce the household’s income uncertainty and thus reduce their need to save for precautionary reasons irrespective of discount rates (Hubbard et al. 1995; Gruber and Yelowitz 1999; Neumark and Powers 1998; Ziliak 2001). The high replacement rate of income provided by Social Security for low lifetime-income households can reduce their need to save for lifecycle reasons. Aside from decreasing precautionary or lifecycle motives to save, government welfare policies may have additional β€˜direct’ effects on household saving incentives. In order to receive many forms of government assistance, households may not have accumulated assets above the federal or state mandated limits.

It seems from the 2001 study you linked that savings are decreasing with the rise of welfare because, as welfare programs increase, equity limits are being relaxed, allowing people to spend more on vehicle assets (i.e., dumping more money into their cars).

Though the significance level was high, the actual effect seemed to be relatively marginal.