This is correct, and results from the mutual repulsion of the nuclei, shifting the energies of both the bonding and antibonding orbitals up relative to the atomic orbital levels, thereby creating the asymmetric bonding / antibonding levels.

Take a look at this picture:

http://chemwiki.ucdavis.edu/@api/deki/files/10224/bonding_antibonding_Dcylinder.jpg

Now imagine that atomic orbitals (on the left side) have some energy, let's say 0. When bonding and antibonding orbitals ar created, the split is not symmetrical. That means that difference between the 0 and the bonding orbital is usually lower than the difference between 0 and the antibonding orbital.

In the simplest example take a He2 molecule with 4 electrons. You fill the orbitals with electrons and since you have 4 electrons, you completely fill both the bonding and antibonding orbital. The result is that the He2 moelcule is unstable, because of this assymetric split, that makes the energy of the system higher than two separate He atoms.

Read more: http://chemwiki.ucdavis.edu/Theoretical_Chemistry/Chemical_Bonding/Molecular_Orbital_Theory

Consider the molecular hydrogen, H2. It is formed by two H atoms, each with an electron in the 1s orbital. As the two hydrogens come together, the atomic orbitals mix in a both a constructive and destructive manner, leading to two orbitals, one stabilized, which is the bonding orbital, and one destabilized, which is the antibonding orbital.

Let's take some arbitrary numbers. If we take the atomic orbitals of the individual H atoms to have an energy of 0, then the bonding orbital will have an energy of -0.5 while the antibonding orbital will have an energy of 1.0. (Remember, these are arbitrary numbers.)

Why is this the case?

First, a few terms. Let's call Haa the energy of the isolated 1s atomic orbitals. Let's call Hab a stabilizing term (it has a negative sign) which comes about from the interaction of the two 1s atomic orbitals forming the sigma orbital in H2. Finally, lets call S the overlap, which is a measure of how much the two 1s orbitals overlap in the bonding region of H2.

The energy of the bonding orbital can be calculated as

E1 = (Haa+Hab)/(1+S)

The energy of the antibonding orbital can be calculated as

E2 = (Haa-Hab)/(1-S)

The denominator in those terms is the main reason. The (1-S) denominator for E2 causes the E2 term to have a greater absolute value than E1 (which has a 1+S term in the denominator).

The numerators make a difference as well, but the denominators dominate the difference.