It is not hard in an oligarchy to act like a monopoly.
http://www.americanprogress.org/issues/2009/06/pdf/health_co...
Oligopolies do tend to be correlated with monopolistic pricing, but I'm not sure they allow it in an otherwise competitive market. Most oligopolies which successfully raise prices tend to be in uncompetitive markets, e.g. cell or cable service, and the price increases may be caused by the hindered competition rather than the oligopoly itself.
Consider the case of an oligopoly in the DRAM market: when they tried to raise the price of DRAM (2001-2002), they succeeded for a short time. They also collectively lost 3.3% of market share over those 2 years and members of the oligopoly (Hynix was the first, I think) quickly broke ranks in pursuit of increased profits.
http://findarticles.com/p/articles/mi_m0EIN/is_2002_Dec_17/a...
The combined market share of the largest and second largest insurer provider goes below 50% only in four states. It goes below 60% in only 5 states. That makes a combined 9 states out of 52 or so where there might not be an oligopoly. There are 19 states where their combined share is above 70% and I have used that cut off line strictly, not counting for example 69%.
So yeah, it might be very competitive in 4 states, ok maybe in 9 states. These states seem to be the one I recognise such as California where the combined share is the lowest at 44%, but it seems that for the vast majority of people the market is hardly "very competitive" or competitive at all.
Also, a market can be highly competitive even if it supports an oligopoly. It may simply be the case that the oligopoly is outcompeting smaller players. See, for example, DRAM, PC's, cars (ignoring their recent bailout), big box retail stores.
I am not saying that the market is or is not highly competitive. Personally with seeing such share markets of 80% and 90% and one even 98% I think they hardly differ much from monopolies especially since unlike internet businesses there is I would think a high barrier to entry and unlike PCs it is not a new market.
As for retail stores, at least in the UK, they hardly are competitive. We hear of price fixing all the time. They just engage in some game where they lower the prices by a penny and put them up by ten pence etc.
But in any event my point was not to conclude whether the market is or not competitive, but only to provide and alternative.
Incidentally, counting states is a bad approach. 1.1% of the US population lives in states where the top 2 insurers have at least 90% market share. The 4 states you described as being competitive (CA, NY, FL, Oregon) account for 25% of the population of the US.
In retrospect, this is roughly what you'd expect. You can't sell health insurance across state lines. Small states can only support one insurance company (due to the fixed costs of hiring actuaries), while big states can support many. So after some thought, I suppose you are right, and the oligopoly model probably does apply to insurers in small states.