I noticed that in a lot of the wood data I see, the modulus of elasticity is printed for bending tests, not compressive.
According to the Wood Handbook (which is referenced by Mark's Handbook) when measured parallel to the grain and with a 12% moisture content, Basswood has a compressive strength of 15,300 kPa and a bending elastic modulus of 1040 ksi (7,200 MPa).
Balsa lists with a compressive strength, parallel to the grain with 12% moisture content, of 2160 psi (14,900 kPa) and a bending elastic modulus of 490 ksi (3,400 MPa)
I know there's a thread around here somewhere that has the link to a free download of the handbook.