Pathological cases could arise for example. The altitude has negative effect on temperature, but the altitude could have also negative impact on the degree of humidity in the air, which could have a negative effect on the temperature (as strange as it may seem, but this is an illustrative case).

In this scenario the altitude would directly inhibit the temperature and indirectly improve it, which would result in a statistical independence between altitude and temperature by coincidence even if it is well known that altitude causes temperature.