The standard response correctly says that none of this matters. The atmospheric GHE is what it is, and is no less true if it turns out that the allusion to greenhouses is inaccurate. Wikipedia takes this approach, with a refreshing brevity and directness.
However, there is a little more to the story (which still says nothing about the truth of the GHE). Greenhouses do work mainly by blocking heat loss through convection. But IR flux blocking is not totally insignificant.
Wood's experimentThe description of this in the 1909 Philosophical Magazine is indeed brief. Some people give the impression that he built a greenhouse out of rock salt, but the geometry seems to be simpler and on a much smaller scale. Still, he concluded:
It seems to me very doubtful if the atmosphere is warmed to any great extent by absorbing the radiation from the ground, even under the most favourable conditions.
This final statement is little emphasised, but seems to be amply justified by the sketchiness of the note:
I do not pretend to have gone very deeply into the matter, and publish this note merely to draw attention to the fact that trapped radiation appears to play but a very small part in the actual cases with which we are familiar.
Indeed he didn't.
Modern GreenhousesIronically, the situation that forced Wood to use rock salt as an IR-permeable material is now reversed. In his day, greenhouses were always made of IR-blocking glass. Now they are often made of IR-permeable plastic. And, in support of Wood, they do work. They block convective heat transport, and also provide an insulating effect to limit conduction through the boundary.
A real greenhouse issueA covering that blocks IR actually makes a real improvement to greenhouse efficiency. It is more expensive, and people are willing to pay for it. Here are some industry observations:
NSW Ag Dept:
For example, films may be used to exclude ultra violet (UV) light for chemical free pest control or reflect long wave infra red (IR) radiation to improve heat retention at night. ... Long wave radiation (2500-40000 nm) absorbers reduce the loss of heat radiated from materials and objects (including plants) inside the greenhouse.
Or this advice
You can also buy a plastic film with an infrared inhibitor; it cuts heat loss inside the greenhouse by up to 20% on a cloudless night.
Actually, it would also cut loss on a clear day.
And here is a pamphlet which describes the practicality in some detail (for heated greenhouses, but the principle is the same).
The IR / anti-condensation treated films cost about $0.015 per square foot more than untreated films but reduce energy use by 15 to 20%.
Scale IssuesThe main thing wrong with the Wood's style reasoning is scale. IR blocking is a minor effect on the scale of a greenhouse because convection is relatively much more effective. The temperature gradients are huge compared to what is maintained in the atmosphere. Wood compounded this by experimenting on a much smaller scale again.
In the atmosphere, IR transport is more important than convection, so the blocking effect of GHG's matters much more.