This is an outdated view. Observations and analyses made in the early 1990s tended to support this view but since then the different observations have been brought into agreement. More ….
It is true that in the early 1990s initial estimates of temperatures in the lowest part of the Earth's atmosphere, based on measurements taken by satellites and weather balloons, did not mesh with the temperature rises seen at the Earth's surface. However these discrepancies were found to be related to problems with how the data were gathered and analysed and have now largely been resolved.
Our understanding of mankind-induced global warming leads us to expect that both the lower atmosphere (troposphere), where most greenhouse gases are found, and the surface of the Earth should warm. Simultaneously the lower stratosphere, just above the greenhouse gas ‘blanket’, should cool.
At first, satellites and weather balloons seemed to show that virtually no warming was happening in the troposphere. However, this has been found to be due to errors in the data. Satellites were found, for example, to be slowing down and consequently orbiting slightly lower, leading to inconsistencies in their measurements. Variations between the instruments onboard different satellites (and weather balloons) also led to discrepancies. Furthermore, a mathematical error meant that satellites showed less warming in the troposphere. However, once the data were corrected, the troposphere temperature was shown to be broadly consistent with the Earth’s surface temperature.
Some discrepancies remain between the temperature that computer models predict at the surface and in the troposphere and what we actually observe. However, these discrepancies are less than the likely remaining uncertainties in the observations and the models.