I totally agree with Eliot.
What you are referring to might be the way the japanese kana し/シ (shi) used to be romanized before World War II.
As a matter of fact, roman-ji was not widely thaught in schools before and there were many standardized and non-standard conversion systems... Indeed, according to some systems it is/was possible to write the "shi"-sound as "si". (and some people still do! My Sensei, whose name is Shigeru, signs "Sigeru")
The things changed when digital typing rules (i.e. keyboards) were to be made. In the Computer Age, a standard romanization system is necessary. Just think about how your computer converts what you type in latin alphabet to Hiragana, Katakana and Kanji.
*There are many other examples of this, e.g.
ち - chi = ti
じ - ji = zi
ふ - fu = hu
つ - tsu = tu
づ - zu = du