Tosfos (Gitin 71a d"h v'ha) writes that submitting eidus via a letter (or other written communication) is OK (according to the gemara's hava amina) even though writing the parsha of chalitza cannot substitute for reading it. The difference is that with respect to eidus, the Torah uses the term "haggadah," while with respect to chalitzah, the Torah uses the term "amira." The term "haggadah" is inclusive of all types of communication; the term "amira" means specifically speaking.
Chasam Sofer in his teshuvos and his chiddusim challenges Tos. assertion based on our parsha. "Vayomer Yisro..." -- "amira" -- according to Ramban (and one view in the Mechilta) means that Yisro sent a letter, proving that "amira" can refer to written communication as well.
The focal point of the machlokes seems to be whether kesivah k'dibur or not -- when halacha refers to speaking or communicating, does writing count? According to Tos. and R' Elazar haModai, "amira" means specifically speaking; "VaYomer Yisro" means Yisro sent a messenger to speak. According to Ramban/R' Yehoshua, "amira" can be accomplished through writing as well.
R' Noson Gestetner in his L'Horos Noson has a clever explanation of the views in the Mechilta as being l'shitasam of another issue. He does this in three steps: 1) Logically, there is no reason that speaking should have more legal significance than writing. In fact, reason seems to dictate the reverse -- if you put something in writing, it carries more weight. 2) The gemara (Zevachim 116) quotes a machlokes between these same two Tanaim quoted in the Mechilta-- R' Yehoshua and R' Elazar haModai -- whether Yisro came before mattan Torah or afterwards. 3) The l'shitasam: Everyone agrees that halachic "amira" means speech and only speech. However, R' Yehoshua holds that Yisro came pre-mattan Torah, and therefore he is free to read "amira" according to its colloquial, non-halachic use which encompasses even written communication. R' Elazar haModai l'shitaso that Yisro came post-mattan Torah must read "amira" consistent with its technical halachic definition as referring to speech alone.
(I'll save some of you the trouble of commenting that the narrative of "Vayomer Yisro.." is not a din and maybe shouldn't forced to fit into halachic boxes. Point granted -- but you can appreciate the cleverness of it anyway.)