There are two factors at play. The first is glass envelope temperature, this is affected by airflow, how much energy it absorbs, cleanliness of the glass, and airflow. This relies on convection, it may be affected by mounting orientation (it may actually get better airflow with the chimney effect of vertical mounting vs the turbulence of a horizontal cylinder - I don't know). This is the minor factor anyway, as long as the pin seals don't overheat. The max pin seal temperature is normally around 150-200'C.
The major factor is thermal (IR) radiation. Becaues of their high operating temperature and the internal vacuum, the anodes dissipate the vast majority of their heat by IR radiation, directly heating bodies that they can 'see'. The manufactur spacing advice is based on this. If two tubes are spaced too close together, their anodes will mutually heat each other, raising both of their temperatures. This effect is independent of mounting orientation.
If you de-rate the anode dissipation of the tubes, you can mount them closer.