I was also taught that the "do" is implied, so I agree that either form you mentioned should be correct. I got it wrong with "as much as I" as well.
However, though the first person form of this implied verb probably gets the most acceptance, in generalizing a bit (in the spirit of teaching a language) we have to consider "She reads as much as he", vs. "She reads as much as he does". I think most people would find the latter less awkward and dangling, even if both are correct. So deeming the latter more 'acceptable' seems reasonable.
"She reads as much as him" (the analog of "He reads as much as me") can get lambasted for being grammatically impure, but it gets a lot of use in the real world among native english speakers - at least in america.
I think a lot of this comes down to the balance of teaching a language and teaching grammar.
Many of the comments here claim that "as much as me" is categorically incorrect English. That is simply not the case. In fact, all three forms: "as much as me," "as much as I," and "as much as I do" are acceptable in standard English.
This problem arises because "as" can be either a conjunction or a preposition, depending on context. Without a verb at the end of the sentence, it is not clear from context whether we are looking at a prepositional phrase or a conjunction. Clearly, not everyone agrees on this, but in Standard English, when the verb at the end is omitted, "as" can be followed by either "me" or "I".
This issue applies to the use of "than" as well, since it can also be used as either a conjunction or a preposition.
For detailed information, refer to this article: http://www.quickanddirtytips.com/education/grammar/than-i-versus-than-me
This article does point out that, while "than me" is acceptable, it's best to avoid it in formal writing because there are many grammarians who disagree with its use.
You can also look through these two discussions: http://english.stackexchange.com/questions/183150/as-much-as-you-and-i-vs-as-much-as-you-and-me http://english.stackexchange.com/questions/3447/i-can-run-faster-than-1-him-2-he
As much as I (do) is a common comparison expression that can be used in a variety of expressions. He reads as much as I do, He eats as much as I do, He works as much as I do. I have heard many such expressions all my life. This type of comparison is expressed as tanto como in Spanish. Certainly many people do say as much as me. Without getting into a discussion of when common speech elevates what used to be a grammar rules into a new rule and whether this case has met that criteria, let me just say this. . Whatever the Status of these rules, there certainly have been taught in school recently enough to have a significant portion of the population use them, if not exclusively, at least in more formal settings. They should therefore be well understood. The advantage of many of the older grammar rules in English is that they often will match constructions in the new language. So whether or not I would say as much as me, if I remember as much as I and say tanto como yo. As English blurs distinctions between subject and object forms it makes it harder to learn languages that do not.
The idea is to limit correct responses. So common expressions are translated into their equivalents, and the strange or unusual sentences are translated as directly as possible without trying to figure out how to make it make more sense. That part is sort of like a diplomatic translator. It becomes important not to add any of your own spin or assumptions. If you translate in the immersion section there is more leeway. The good literary translator has to include the same elements of flow and feeling as the original. But that section is not computer scored either.
There are three como, although one is just the 1st person conjugation of the verb to eat. The second is Cómo which means how. It is the interrogative pronoun. Como without the accent means like or as as an adverb. It can also be a conjunction meaning as/since or if.
You will notice that all the interrogative words in Spanish have the accent even though the accent doesn't alter the stressed syllable at all. This is because each has a twin word without the accent. This word is often a relative pronoun or other part of speech. Some like this one and qué/que have different English translations, but many translate to the same word in English, although they play different roles in the sentence. That can make them hard to recognize sometimes.