Dispersion forces - what determines which molecule will have its electron cloud repelled?
You are correct that the electron clouds would repel each other equally.

The induction as shown in your second picture would require another outside entity, polarizing one of the He atoms, which would then affect the other.

At an arbitrarily show distance, we might describe a molecular orbital formation between the two helium nuclei, as shown here:


(source: mhhe.com)  

In this case, without the external perubation, the orbital shape (and hence the electron clouds) is (are) quite symmetrically distorted.

However, it becomes nonesense to describe a system of two atoms.  In liquid helium there are manifold other charge fields distorting these nice shapes, and you may get some asymmetry as shown in your picture above.