Si is actually fairly non-reactive at normal temperatures and in a normal atmosphere once the native atmospheic SiO2 layer is formed and that forms very quickly, on the order of a few minutes. It takes a lot to make Si react. There are ways to make Si react but not with out a lot of effort using some fairly exotic techniques-high temeperatures with steam to add more SiO2 or high temperatures with pure HCL gas flowing across the Si surface or in an RF plasma with SiF6 gas enetering the plama chamber.
Single crystal Si is usually grown from a melt(~1350 C) of amorphus or polycrytalline Si into which a seed crystal of the specific lattice orientaion desired—1,1,1 or 1,0,0 or 1,0,1, or 1,1,0, etc —is lowered while kept spinning and the slowly withdrwn from the melt.Much trouble is taken to keep all impurities out of the melt but you still get some gasses and other elements trapped in the crystal lattice. The Si for the balls may be produced in a different manner but most semiconductor Si is produced as I described.
So, yes Si is reactive But not by just sitting around in the vault at room temperature that these standards will be kept or by normal handling. I doubt that anyone would be allowed to touch them with bare hands after they are “complete”.
SiF6 should be SF6