I consider the popular argument of Medicaid crowding out demand for private long-term care insurance. I show that this argument rests on a wrong counterfactual comparison. Furthermore, I question the welfare-decreasing impact of Medicaid as it neglects a large value of the program in providing access to care. I show that private insurance is unable to offer a similar value. I posit that the low take-up of private insurance is due to a dilemma prevalent in - but not exclusive to - the market for long term care insurance: a dilemma between access and affordability. Several empirical patterns in insurance uptake and lapsing behavior can be explained by considering the issue of limited affordability.