So in this example if you searched for the English word "Eat" that is also a completely legal Russian word (E, A, and T, exist in English and Russian), however it means nothing remotely similar.
I don't know if they're right or wrong. I am just saying that might be the point they were trying to make. You could make a Greco Unified unicode set and it would work fairly well, but you might wind up with some confusing edge cases where it isn't clear what language you're reading (literally).
This could be particularly problematic for automation (e.g. language detection). Since in some situations any Greco-like language could look similar to any other (in particular as the text gets shorter).
For simple alphabet-type languages, the basic rule should be: if the uppercase and lowercase look the same, then unify mercilessly. P (English) and Р (Russian) should unify even though they represent different consonants. But not V (English) and В (Russian): they sound the same, but have totally different graphemes. On the other hand, unifying B (English) and В (Russian) does not make sense: the lowercase forms look different: b (English) and в (Russian).
Sounds like the major problem with Unicode (and the author's complaints) was always where to draw the line. Han unification went too far and included too many characters that look different. With other languages, some common combinable characters were forced into diacritic representation rather than getting their own code points. To me, the first problem seems way more serious.
For languages that would be affected by a greco-unification that meant the encodings that were in use before unicode had both the latin script and their "national" script.
Implementing greco-unification in unicode would mean that round-trip lossless conversion (from origin encoding to unicode back into origin encoding) would be impossible, greatly limiting unicode's adoption.
No such problem existed with han characters, in fact JIS X 0208 (the character set used for Shift-JIS) did a very similar thing to unicode's han unification.
In absence of backwards compatibility problems I would be in favor of greco-unification too.