Edit: TL;DR: it's complicated.
Quite true (with caveats). Additionally there's the cost of energy distribution (one source I see quotes this at 10% loss, another quotes ~6.1%).
In the one case you have the combustion engine (or equivalent) in a car. The benefit here is that the fuel energy is spent to produce kinetic energy and (waste) heat, with minimal-to-no conversion losses. Downsides include only a limited subsets of fuel are available (petrol, diesel, some others) - some are fossils, some are renewable but controversial bio-fuels. Some fuels are simply not available/practical in all situations (nuclear, hydro-electric, solar(?) etc.).
In the other case you have electrically stored energy, which involves the aforementioned conversion/distribution losses - which are significant. But this isn't the whole story.
* When braking, an electrical vehicle can translate at least some of the kinetic energy back into stored energy .
* Central electrical generation facilities can potentially produce electricity at a greater efficiency with the benefit of scale production, and not having to make compromises to limit vehicle mass. 
* Whilst traditional vehicles rely on a limited set of power storage/generation fuels (typically combustion/carbon-based), electricals are not limited to these sources. Therefore, this is an apples/oranges comparison without a deeper insight.
On this last point, the question is how the additional electrical energy is produced to charge vehicles. This is complicated by the ratio of electrical generation changing over the course of the day, and from day to day:
* often gas-fired plants being fired up to make up extra power during peak times, (also stored hydroelectric power, but that's effectively generated from off-peak and slack generation capacity),
* nuclear and coal creating a large baseline of electrical generation capacity,
* solar, wind power generation, as weather, tides etc. allow (we're at the mercy of nature on this, with some level of predictability),
* "other" - my catchall bucket for everything else.
Ideally we'll move towards the renewable and clean sources over time, ones which don't incur long-term and potentially catastrophic (certainly contraversial nuclear fission). Nuclear fusion is an interesting and real possibility, but does not in the near-term (~10 years) provide a sustained and power-positive reaction.
The key here is that electrical cars have the potential to be effectively clean-"burn". The present electrical generation notwithstanding.
All that said: I'm neutral on electrical cars (I have no financial or other interests in cars or electrical generation - I don't actually drive a car - ha!).
Edit: One minor thing electrical cars certainly do is move the combustion pollution from the cities/urban areas out to the power plants. This is probably more of a human health argument than anything else. It's probably something that will be measured more in retrospect, such as the (sometimes unexpected) effects of (for example) smoking bans.