He was correct. Lead oxide isn't formed.

There's several factors that need to be considered. The fact that the Lead-214 daughter is singly ionized so reactions with oxygen aren't favoured, that air is humid and is often contaminated with VOCs and SO2, especially indoor air, and the fact that these reactions take place within an ionization trail generated by the Alpha particle, that generates hydroxy radicals from atmospheric humidity and NO2 (the radon daughter atoms recoil at 10-13 million mph btw).

Instead, Lead-214 will most often form tiny clusters surrounded by 5 to 8 water molecules and likely often a few molecules of VOCs. They measured the size of the clusters, they average 1.2 - 2 nm in diameter. Po-218 is a little different, it forms larger 15 nm clusters additionally with SO2 (once air contains a few ppm of SO2) and as, well as much smaller clusters of PoOx 0.5 - 1 nm in diameter (the proportion of these clusters depends on what's in the air).

Castleman Jr, A.W., 1991. Consideration of the chemistry of radon progeny. Environmental science & technology, 25(4), pp.730-735.

Hopke, P., 1996. The initial atmospheric behavior of radon decay products. Journal of Radioanalytical and Nuclear Chemistry, 203(2), pp.353-375.