This is absolutely incorrect- this describes a wavetable synthesizer, which is what the early Kurzweil's were. An additive synthesizer works by adding individual sine waves together of various amplitudes and frequencies.
The other famous additive synth was the DKI Synergy. It was a preset-only version of the ludicrously expensive Crumar GDS ($27,500), although if hung a Keypro micro off it you could create your own sounds without the GDS.
The Kawaii additive synths came a lot later.
The most recent additive outing is Camel's Alchemy, which does additive and other synthesis types. It which was bought by Apple and bundled with Logic Pro 10.2. NI's Razor is also additive, although the programming model is strange.
Additive can sound amazing but it's incredibly tweaky and time-consuming to program, so most people still prefer subtractive/analog.
It sounds like nothing else out there, don't think I'll ever get rid of it.