Good info. I already knew all this because I've been shipping with UPS and FedEx for more than 10 years. You can ship tire/wheel packages via Ground (discounttiredirect and tirerack do this) but I doubt they will let you ship them air. That's dangerous. Hell, they won't even let you ship most bug spray via air because it is considered ORMD.
Note: If you ship on your work UPS or FedEx account and don't weigh them properly or dimensionalize them, the account you used will get billed for them. You might very well get away with it depending on how diligent your accounting team is but it's something to be considered.