But U.S. oil companies do not have the power to manipulate prices to impact elections.

I don't support the view that prices are currently being manipulated. However, the claim that the market cannot be manipulated is highly dubious. There is a plausible mechanism of manipulation, which was discussed in the context of mid-term elections in 2006:

In addition to the issue of index funds accumulating long positions and thereby imputing an upward bias to commodities, there is another opportunity for market manipulation with respect to the construction and rebalancing of prominent commodity benchmarks such as the Goldman Sachs Commodity Index (GSCI).

As reported by the New York Times on September 30, 2006 Goldman Sachs significantly readjusted in August of that year the GSCI's gasoline weighting. Index products tracking the GSCI, and representing an estimated $60 billion in institutional investor funds, were forced to rebalance their portfolios resulting in an unwinding of positions. Originally, unleaded gasoline made up 8.75 percent of the GSCI as of 6/30/2006 , but this was changed to just 2.3 percent, representing a sell-off of more than $6 billion in futures contracts.

As a result, gasoline fell 82 cent in the wholesale market over a four-week period, an unprecedented move; and crude oil, which in July 2006 traded over $79 per barrel for August delivery—at the time an all-time record—subsequently fell to around $56 by January 2007.

Many at the time argued that these moves were due to fundamentals, but… it should also be noted that the U.S. was in the midst of mid-term elections with Republicans facing a major fight to retain control over both Houses. According to a Gallup poll at the time, 42% of respondents thought that the Bush administration “deliberately manipulated the price of gasoline so that it would decrease before the elections.”Source

The NY Times discussing this same phenomenon: Change in Goldman Index Played Role in Gasoline Price Drop

Matt Simmons himself has stated that:

Effectively, the changing perceptions of a small handful of speculators now appear to set the price for West Texas Intermediate crude oil, which in turn sets the general price for almost all other crude grades throughout the world.

If this is true, the world's most important commodity is being priced by a handful of hedge funds or individual speculators who, as a group, invest less than $100 to $150 million at any period of time.Source(pdf)

If you want to state that the market cannot be manipulated, and is not powerfully affected by speculators, you should directly address the more plausible mechanism noted above, and the arguments given by Simmons in the above paper. Personally, I wouldn't use the term "manipulation", but I would claim that speculators and other purely financial interests play a very large role in the market, going both up and down. Given that the entire financial system is rife with financial excesses and chicanery, I find it highly unlikely that the oil market is a temple of purity.