The solution is analogous in many ways to a class of solutions that represent the creation of virtual particle/anti-particle pairs from the vacuum. We understand that process quite well - the "vacuum" of a quantum field theory is never truly empty due to random fluctuations of the fields.
To make an analogy, think of a field as something like air - it fills all space. There's a field corresponding to each species of particle (electrons, quarks, photons, etc.). Localized "sound" pulses (wavepackets) in the "air" (field) are particles. So the state with zero particles is a state where the field is completely homogeneous and constant. But quantum mechanical uncertainties and zero-point energies mean that at any moment there are always going to be some insuppressible little ripples propagating around - so if you make a sufficiently precise measurement, you'll detect some particles even in what you thought was a perfect vacuum.
(Incidentally, the creation and annihilation of these particles conserves energy for a very similar reason that Hawking's solution - and the resulting universe - does.)
So what's the problem? The problem is that for particles there is a classical vacuum - a state with zero particles - on top of which there are these quantum fluctuations (states with more than zero particles). But we don't know what the analogue of the vacuum is for universes. We don't understand how to formulate a theory in which the number of universes can vary, with a zero-universe vacuum plus fluctuations (technically such a structure would be called a Fock space of universes).
Because we don't understand that basic piece of the theory, any interpretation of Hawking's solution as representing the creation of a universe from nothing is speculation. It's not completely unfounded, because the analogy to particle creation is mathematically fairly precise, but it remains speculation.