Thanks for the link, okie.
Let's have a look at the data and the map in the article:
The rates of people without insurance is, in fact, pretty high in counties along the border. Now, simplify things, let's assume that those people without health insurance are not more often in need of health care than people with health insurance. (I acknowledge that in some areas there might be a higher need for health care among immigrants, but it would be offset to a certain degree by the lower average age of that population.)
Then, let's assume that all those people without health insurance
never pay a single cent for health care out of their own pockets. Let's assume all of the cost for their health care has to be shouldered by those who
do pay into a health insurance.
(As McGentrix said earlier, the costs are not really offset by people paying health insurance, but via taxes - so let's also assume that those without health insurance
never pay a single cent in taxes.)
Given those preconditions, that would mean that without those people who don't have health insurance, health care costs for the average American would be lower by the percentage of people without health insurance.
So, the OECD statistics pegged the per capita health care costs for Americans at $6,401. Let's subtract the complete 14.2 percent of all those people without health insurance - and you're left with per capita costs of $5,492.
Still the highest in the world. Still $2,733 above the OECD average.
(And all of that is not taking into account that there are not only immigrants, but also Americans without health insurance. And that immigrants
might pay for some of their health care costs out of their own pockets. And that they
might be paying at least some taxes, which would offset the costs on the ERs at least to
some degree.)