Radioactive decay is not the only way to make lead, and lead is produced in much greater abundance than uranium.
The part that’s missing in the post is in looking specifically at uranium deposits and making assumptions about the initial composition of the deposits, since the crystalline structure excludes lead when the crystals form. So if you detect lead contained within zircon, it is assumed to be the product of radioactive decay.
Were they drinking soda in a lab room filled with fissile material?