From a physics standpoint, this is not true. Larger reactors help you have higher total neutron cross sections, both for elastic scattering / moderation and fission. A "small" nuclear reactor is defined by the IAEA as one that's less than 300MWe, although even reactors as big as 500MWe are sometimes referred to as "small". Per-reactor, not per-plant. Don't get me wrong, you can make reactors at any size - some companies are looking at modules as small as 25MW (per reactor). But it makes your already problematic economics even worse.
That said, I still do have more hope for small reactors than large ones, just simply from the standpoint of getting some degree of mass production and refinement through use. Still, the "nothing may go wrong" situation one faces with nuclear reactors and the "need to start from scratch if some flaw is developed in the basic design that prevents you from 'nothing may go wrong'" still bites.
Not to mention the effects of scaling on the steam turbine. In general, the larger the turbine, the more efficient it is, both thermodynamically and from a total cost of ownership standpoint. The choice of technology / vendors in any power plant today is generally picked by accountants running Net Present Value-type calculations.