If we're to go by Occam's razor, there's no reason to believe in this theory. It makes more assumptions than the conventionally held account of Kohji's death does. That being said, Gosho Aoyama is a mystery writer; unexpected twists are what he does best. If everything in Detective Conan was predictable, it wouldn't be as interesting as it is, and he already has pulled the wool over our eyes on seemingly solved cases ("Mizunashi Rena cannot be Eisuke's sister because they've got different blood types. Well, case closed. Time to move on to the hospital showdown). Given this, it's possible that Aoyama may go down this route precisely because it's unexpected.
Shiho spent a great deal of her life in the United States, a country where English is the only official language. Given this fact, she most likely speaks English as a second language. Even though this is probably the case, she doesn't seem to have a full mastery of the language. For instance, whenever Conan said "Vermouth" to her, she didn't react at all. Whenever he said "Belmot" (the Japanese name for this given alcoholic beverage), she panicked. Either she knew the Japanese name for the beverage (Belmot) but not its English equivalent (Vermouth) or she didn't recognise the alcohol in question and only heard the word Belmot from BO agents as the codename of that youthful 50 year old woman.
There's nothing to suggest that, prior to his trip to the United States, Kohji Haneda spent any time at all in an English-speaking country. Assuming that Asaka is a Japanese name (a Japanese person who was working for an American client would likely know both languages), it's possible that Kohji didn't have to learn any English at all for his trip to America and that Asaka would serve as a translator.
In short, if a person who had spent much of her life in America only knew the Japanese name for a given alcoholic beverage, it's not a stretch to assume that likewise, Kohji would not know the English name of certain alcoholic beverages. The beverage in question is called "Rum" in English. In Japanese it's "Ramu".
Despite this, he might know of the Latin alphabet, which is used for English and a variety of other languages. Ramu is a foreign import word, since Rum did not originate in Japan or its nearby neighbors. Given this, in Japanese it would be spelled with katakana characters (I've confirmed that ramu is spelled with two katakana characters). The two characters were for the "ra" and "mu" sounds, obviously. And of course even words which are spelled with kanji can be spelled with katakana. Given this, even without a grasp of the English language Kohji would likely be able to spell this Japanese word, and others, in the Latin alphabet if he simply knew that much.
Whenever creating his dying message, Kohji used a mirror, if I'm not mistaken. It had the following letters:
PUT ON MASCARA
This would be enough letters for whatever message he was trying to create, or else he would've used something other than a mirror.
What we know is that the letters PT ON were eliminated, leaving "U MASCARA".
However, before this point everyone has automatically assumed that Kohji would spell RUM as it appears in English. But what if he wrote RAMU instead? What if the actual message was "ASCA RAMU"? Obviously the ASCA would either have to be rearranged somehow or interpreted as it is (the context of this first word in the dying message is yet unknown).
Whenever Asaka saw the dying message and managed to figure it out, he/she assumed that it read "ASACA RUM", because he/she just naturally assumed that Kohji would spell Rum as in English and didn't consider the spelling difference between the two languages. Given this, Asaka thought he/she was being accused of the crime, so he/she made a run for it.
Problems with this theory:
1. It assumes that Asaka somehow knows who Rum is.
2. Again, ASCA makes no bleeping sense regardless of how it's arranged.