The correctness or lack thereof really depends on how you account for the externalities.
If you only count the reactors that are already built and still operating, they are pretty cheap sources of electricity. The old nuclear projects that were abandoned before completion won't be part of your "power per dollar" denominator. The reactors that were shut down 10 years ago because they were too expensive to keep running will also be missing from the denominator. The late and over-budget reactors that have yet to enter service will be missing from the cost denominator as well. Once you limit the field of inquiry to the surviving, operating nuclear plants, they're pretty affordable.
If you interpret the question as meaning "nuclear energy is currently the second cheapest per watt [to add to a nation's electricity supply]" -- no, that's incorrect for anywhere with half-decent wind or solar resources.
The final question that prevents me from being a 100% renewables triumphalist: what happens to the relative cost of nuclear vs. more renewables + storage as renewable penetration rises? Storage is hardly needed at present penetration levels. Only a modest amount of storage (overnight) may be needed for 50% or even more penetration. But what happens at 80%, 90%, 100% decarbonization of the electricity supply? It's possible that even expensive new reactors will be cheaper than reaching 100% with storage and renewables alone. It remains an open question.
As renewables, getting cheaper, are added and longer term storage becomes needed, nuclear is placed in a horrible position.
That's because nuclear needs to sell its power a high percentage of the time or its economics become ridiculously bad.
So what happens when solar/wind/short term storage are covering things 80% of the time, at a cost (during that period) the nuclear reactor cannot come close to, on a levelized basis? The cost of power from the nuke goes up by a factor of as much as five. Nuclear plants are horrible as intermittent fill-in sources. It instead becomes more economical to add low-efficiency long term storage options (like hydrogen) and to just overbuild the intermittent sources.
Or it could turn out that building very large storage systems, even capacious enough to e.g. ride through Germany's entire winter, is less expensive than building new reactors. I'm just trying to keep an open mind about a future role for new reactors. I'm pretty skeptical about starting new reactor builds right now. My strongest present opinion about power reactors is that it's a shame to close working units while their attached grids are still consuming fossil combustion power.
Small molten salt reactors might also address industrial process heat markets, where they'd have a possible advantage over renewable sources as their heat could be used directly.
A data point in favor of this: Suppose there was a fast developing country that had the resources and requirement to build more power generation capacity than any other society in human history. Suppose, further, that this country was relatively immune to political concerns because it was governed by a technocratic bureaucracy. Just for the hell of it, let’s imagine that most of the techno-bureaucrats have some sort of engineering background. It so turns out that there is a country exactly like this, and their long term energy policy is to build a massive hydroelectric dam on the one place in their country that is particularly well-suited for it, and then build lots and lots and lots of fission plants and invest in fusion research.
UK discounted provision for decommission costs: £100+ billion in 2013 https://www.theguardian.com/environment/2013/jun/23/britain-...
£161 billion in 2017 https://web.archive.org/web/20170516093449/https://www.gov.u...
£234 billion in 2018 https://www.gov.uk/government/publications/nuclear-provision...
... and counting.
UK: 15 reactors, ~10300 gross MWe. They analyzed and now think that decommissioning will cost £234 billion (309 billion USD).
USA: 98 reactors, 100350 gross MWe. 46 billion USD (Nuclear Waste Fund) are in provision.
One order of magnitude more power produced by the stuff to decommission in the US, and nearly 7 times less money to do so.
Decommissioning small and old reactors costs more, and entombing may, at least apparently (short-term), reduce the cost. In theory. Let's check a real and ongoing case: Oyster Creek. According to the EIA its construction costs were $488 million (2007 USD) ( https://www.eia.gov/nuclear/state/archive/2010/newjersey/ ). As soon as the decommission project started the Nuclear Regulatory Commission announced that it will cost "about $1.4 billion to shut down the plant". Not for an immediate and complete decommission, because the plant will stay in a “safe store” condition until 2075, with dismantling ((...)) set for a period between 2075 and 2078 ( https://www.powermag.com/oldest-u-s-nuclear-plant-shuts-down... ). Then new problems (costs!) may arise. Let's bet that, as usual, the taxpayer will pay.
Long-term waste management is another ticking bomb.
Moreover if there is a serious glitch (Chernobyl, Fukushima...), are bets are off. You can obtain an insurance policy for anything, AFAIK even for a space trip, but no insurance company covers such nuke risk.
If they only knew how much they get from bananas, granite counter tops, and airplane trips in comparison to nuclear power and scaled their fear of radiation down to that level, most of these expensive problems would be 100 times cheaper to deal with. How about a massive education campaign about radiation starting in elementary school? Kill the fear. Isn't the whole point of education is that an educated public can make better choices? Let's use that tool.