I'm afraid that is not true. When you study all the countries with single payer, you will see that they vary considerably. Many do not have gatekeepers at all. Some have very small co-pays as well, without high deductibles. So it depends on which country you look at.
Video: Sick Around the World | Watch FRONTLINE Online | PBS Video
As for the high deductible plans for the poor. I agree with another poster on their point to a degree. Unfortunately, IMO for someone who is really low income and has been using a free clinic or county hospital for their care, I don't think having to purchase a plan that would cost them even $100 (with subsidy) a month is going to be very appealing to them, when there is such a large deductible that comes with it. Also, consider if they have no assets, are renting and live pay check to pay check, they are not exactly afraid of "losing it all" if they get sick.
So unless there is a plan for them that is very reasonable, where they can get actual care and medicine when there sick, I don't think the incentive is there to buy a high deductible plan. I am in favor of what the ACA has brought us in terms of stopping the outrageous practices of the insurance companies. But in terms of getting the lower income people to purchase plans, I don't think it will succeed based on the type of plans I see offered for them that are reasonable in cost.
I don't know how representative we are here in Missouri, but there are some plans in my metro area that might be reasonable. For example, the lowest cost Silver plan ($16000 MAGI, age 57 male) from Coventry One has a premium of $45/mo, and a zero deductible! No charge for PCP OV's, and $5 generics. But you may be right, that some people are sufficiently satisfied with the low or no cost clinic/public hospital option instead. Having worked in those environments, that is not my impression -- but I encountered a lot of unhappy patients in the elite suburban hospitals, too! I guess we'll see...