That thesis is rather subjective, and many assertive individuals including in climate science could potentially be accused of being too cocky about their own work. I would say however it is the would-be climate skeptic camp that actually is more lacking in both skpeticism and self-review. My point here though is to address a mistaken theme, that computer climate models are the lynchpin of climate science and are highly flawed.
Starting with a quote,
"[T]he main basis of the claim that man’s release of greenhouse gases is the cause of the warming is based almost entirely upon climate models."
Regardless of who is saying it, this statement is not accurate. A good resource for learning about climate science is Spencer Weart's The Discovery of Global Warming. In particular see the section focused on carbon dioxide and the summary section on climate change. Climate models are very useful tools for investigating climate change, but they are hardly the main basis of knowledge about climate change.
The links above describe the multiple converging lines of evidence form the basis of the understanding anthropogenic greenhouse gases are causing warming. The heat-trapping and thus warming properties of greenhouse gases including CO2 were studied in the 19th century. We know greenhouse gas concentrations in the atmosphere are increasing and that the increase is due to human activities including burning fossil fuels. Research on past climate variations have helped demonstrate that other processes cause an amplification of warming beyond what the increasing greenhouse gases directly produce.
Saying that climate models are the main basis for asserting anthropogenic greenhouse gases are causing warming is like saying that computer models are the main basis for claims than autumn rains and winter snows cause flooding in the Red River Valley.
The other incorrect assumption regarding climate models is that their quality is undermined by the shortcomings of weather models.
First a brief note about weather prediction. It is a long-established cliche that the weatherman is often wrong. There is the issue of what people expect from weather forecasts and whether they understand what forecasts really mean, but that is a whole other discussion. Actually weather forecasting has improved noticeably over recent decades.
They are basically the same tool, but weather models and climate models do very different tasks. I highly recommend this post for explanations of weather models versus climate models.
A weather model is sort of like taking a snapshot of all the cars on the roads of a town at a given time and trying to figuring where they will be in an hour. In this case the better you know the initial conditions (at the start time who with what driving habits is driving where) the better you will likely be at figuring out who will be where an hour later.
On the other hand a climate model is sort of like taking a snapshot of the layout of a city and determining what general traffic patterns will be like. In this case the better you know the boundary conditions the better you will be able to predict the patterns. For example, if you know that almost all the homes are in one area and most businesses and offices are in another area, you can likely predict that weekday mornings will have a lot of movement away from the homes and return flow in those evenings.
Any particular climate modeling group may view their own a bit too highly, but that would be the same as any researchers in any field. There is no reason to single out climate scientists as a whole for any particular lack of a critical eye to their own work. Climate models are not perfect but are useful and improving tools. I contend there is hardly a problem with overconfidence among climate scientists but rather a problem of public confidence in climate science being unduly undermined by a broad misinformation campaign trying to do exactly that.