As to my best knowledge, the 'ninja-to' is a purely fictional piece of equipment, as despite the large number of weapons and armor of Japanese origin preserved in excellent condition (not to mention even more in various state of decay), there is not a single known specimen of a straight-edged variation of katana. It's popularity in the West most likely dates back to the texts of Stephen Hayes, some of them being translation of the works of his teacher, Masaaki Hatsumi, even though there is no evidence that Hatsumi ever mentioned 'straight swords' in his original texts.

As Stephen Turnbull says in 'Warriors of Medieval Japan' and 'The Ninja: An Invented Tradition?' article, the whole notion of 'ninjas' as we known them today is largely a modern fabrication. 'Special operatives' performing tasks related to reconnaissance and infiltration indeed existed but were regular bushi (warriors), usually regular samurai in the employ of their master who simply had some specific skills set, not the specially trained members of sui generis 'warrior cult' as ninjas are often portrayed in modern popular culture. Furthermore, if we take the look on the historical graphic works, we can see that virtually all of them shows 'spies' carrying regular weaponry. Woodcuts by Utagawa Toyokuni often portray actors and stagehands clad in black, that are precursors to the modern image of ninja. It is most notable in the case of 'Matsumoto Kōshirō, Iwai Hanshirō, and Nakamura Shikan' and 'Suma', both featuring black-clad actors striking from the shadows, obviously portraying assassins. In both cases, they carry normal katanas. Ukiyo-e prints depicting famous cases of infiltration such as those done by Yoshitoshi Tsukioka or Ishikawa Toyonobu show characters (Toyotomi Hideyoshi and Horio Yoshiharu, respectively) during the siege of Inabayama (1567) as regular samurai with similarly dressed and armed bushi as their retinue. Despite popular opinion of the bushido (also a product of late 19th century romanticised work 'Bushido: The Sould of Japan' by Inazo Nitobe, aimed at popularisation of Japanese culture in the west), bushi were warriors, usually driven by combat efficiency. Infiltration, sabotage and similar underhanded tactics were definitely not below their dignity, as evidenced by sieges of Inabayama, Chihaya or Dongnae.

But if we were to form a conjecture, there is one reason why Japanese swords could have been straight. Katanas are usually forged straight from several types of steel, the simples combination consisting of softer steel for the spine and harder steel for the edge. When heated and quenched during hardening, the difference of properties cause them to undergo slightly different austenitic transformation, where, to put it simply softer steel contracts slightly more, causing whole sword to eventually curve back. This could mean that straight sword could have been either made of monosteel (single type of steel) or they were not hardened. Although feasible, this conjecture is grasping at straws at best, because both theories would suggest that such weapons were vastly inferior to even the simplest properly made katana and with scarcity of iron in Japan and resulting price of this material, this is not something one would actually do, especially on a significant scale.