Neoliberalism generally refers not just to a set of economic theory but to a whole political ideology. A common application is the idea that privatising any public assets and reducing regulation will lead to better service and lower cost to consumers, or that lower company taxes will lead to economic growth, but after almost fifty years of this being the mainstream modus operandi in the west this has basically failed every time we've implemented policy based in the ideology. All that happens is that (in aggregate) wealth is shifted more and more towards the already wealthy. So it's not just a misused model, it's a theory and ideology that says it will achieve one thing but consistently does something else (and generally worse for most of society).
An interesting thing about neoliberalism is that it often purports to just be about 'free-market' but isn't really. It actually relies on Government to create a lot of the wealth which is shifted to wealthy people through privatisation, and relies on Government to protect monopolies, subsidise private sector activity etc.
For example, in Australia we have universal healthcare (basically the complete opposite of neoliberalism) that the right-wing of politics has been trying to cut funding to and sell off for the last 30 years or so, but so far have failed (it's political poison). At the same time, anybody can choose to use private hospitals, and to do that you really need health insurance. But our public system is so high quality that in general most people would rather just use that (the main exception being waiting times for elective surgery given underfunding). So to keep the private insurers in business, the Government brought in a health insurance rebate where they basically pay a quarter or so of your health insurance premium. At the same time, if you make a certain salary, you are penalised for not having private health insurance through an extra tax. So most people earning average wage or above do. This is purportedly to take pressure off the public system, but studies have shown that the public system is actually quite a bit more efficient than the private system here.
This latter scheme is based in the neoliberal ideology. Even though it would be a lower cost to society to just divert that rebate into the public system (where every 10c more goes to patient care for dollar spent vs. the private system according to studies), this way the private insurers are subsidised with public funds.