Yes, that's correct. Continuous creation was needed because the original steady state model was in permanent inflationary expansion, and Hoyle, Bondi and Gold (and presumably Narlikar) subscribed to the "perfect cosmological principle", which stated that the universe's average properties were unchanging in space and time. An expanding universe without continuous creation would break the perfect cosmological principle (obviously, the average matter density would tend to decrease). Hence the point thermodynamical violation represented by the big bang's initial singularity was replaced with continous, uniform violation. This can also prevent heat death, because you have an indefinite source of low entropy energy to draw upon.

The model was eventually abandoned after some of the best entertainment available anywhere in published science*. The official successor to the steady state model is a lot more complicated, and as I understand it, oscillates rather than expands continuously.

You might also encounter variants on "static state" cosmologies, where no expansion takes place, and yet the universe is infinitely old (i.e. where the perfect cosmological principle is still held to apply). That model really does have an entropy problem; you can't resort to continous creation because then the average density of the universe would increase (even ignoring gravitational effects), and break the perfect cosmological principle. But without it, you're stuck with an infinitely old closed system, without an external source of low entropy energy. We should be dead in this model.

I've heard that puzzle described as Hilbert's Hotel; I assumed David Hilbert was the first to describe it?

* There are some fantastic arguments in the literature between early big bang supporters and the steady state cosmologists.