You're on the right track: it is a dynamic equilibrium that must be maintained actively, not a chemically automatic equilibrium that occurs passively (without biological action). Excerpts from Wikipedia:
Values of resting membrane potential in most animal cells usually vary between the potassium reversal potential (usually around -80 mV) and around -40 mV. The resting potential in excitable cells (capable of producing action potentials) is usually near -60 mV—more depolarized voltages would lead to spontaneous generation of action potentials. Immature or undifferentiated cells show highly variable values of resting voltage, usually significantly more positive than in differentiated cells. In such cells, the resting potential value correlates with the degree of differentiation: undifferentiated cells in some cases may not show any transmembrane voltage difference at all.
Maintenance of the resting potential can be metabolically costly for a cell because of its requirement for active pumping of ions to counteract losses due to leakage channels. The cost is highest when the cell function requires an especially depolarized value of membrane voltage. For example, the resting potential in daylight-adapted blowfly (Calliphora vicina) photoreceptors can be as high as -30 mV. This elevated membrane potential allows the cells to respond very rapidly to visual inputs; the cost is that maintenance of the resting potential may consume more than 20% of overall cellular ATP.
On the other hand, the high resting potential in undifferentiated cells can be a metabolic advantage. This apparent paradox is resolved by examination of the origin of that resting potential. Little-differentiated cells are characterized by extremely high input resistance, which implies that few leakage channels are present at this stage of cell life. As an apparent result, potassium permeability becomes similar to that for sodium ions, which places resting potential in-between the reversal potentials for sodium and potassium as discussed above. The reduced leakage currents also mean there is little need for active pumping in order to compensate, therefore low metabolic cost. [Emphasis added.]
Thus it turns out that resting potential is an interesting, functionally variable quality of different cells, and sometimes costs quite a bit of energy to maintain!
 Magnuson, D. S., Morassutti, D. J., Staines, W. A., McBurney, M. W., & Marshall, K. C. (1995). In vivo electrophysiological maturation of neurons derived from a multipotent precursor (embryonal carcinoma) cell line. Developmental Brain Research, 84(1), 130–141.
 Juusola, M., Kouvalainen, E., Järvilehto, M., & Weckström, M. (1994). Contrast gain, signal-to-noise ratio, and linearity in light-adapted blowfly photoreceptors. The Journal of General Physiology, 104(3), 593–621. Retrieved from http://europepmc.org/articles/PMC2229225/pdf/jg1043593.pdf.
 Laughlin, S. B., van Steveninck, R. R. D. R., & Anderson, J. C. (1998). The metabolic cost of neural information. Nature Neuroscience, 1(1), 36–41. Retrieved from http://www.nature.com/neuro/journal/v1/n1/full/nn0598_36.html.