That would be a reasonable asumption based on your quote of the FAA Order 8700.1...but,..what's the date on that, and do you know it's current?...and has it been 'updated' to reflect the current FAR.
I know for a fact that the 8700.1 sometimes lags behind in getting changed to reflect FAR changes, particularly Part 61 Certification rules. They are the lowest on the totem pole of 'FAA things to do' list.
Good question. First of all, I'll say that I personally agree with your reading of the reg on both a legal and "sense" level (teaching a single engine instrument approach in a twin doesn't require an CFI-AME?

And, there is a bit of history, including, as I recall, a Eastern Regional FAA legal opinion, that supports your reading.
But...
The version of 8700.1 that blurb comes from includes the revisions through 11-15-05, so it is current. Or, at least as current as it can be - Order 8700.1 was (recently) canceled and replaced by 8900.1 (
http://fsims.faa.gov/). The quoted language has been reproduced without change at para 5-503.
I don't know what the prior 61.195 language was (or even if it was in the same place), but the current 61.195 language goes back to the August 1997 Part 61 revision.
Although it is not mentioned in the part dealing with this, there are in fact revisions to 8700.1 that deal with the the fact that "On August 4, 1997, a complete rewrite of part 61 became effective." (the quote is from a part of 8700.1 that talks about night flying restrictions).
FWIW group, the 8700.1 interpretation is identical to John Lynch's in the officially-disowned Part 61 FAQ which was written specifically to deal with the 1997 revisions.
Even if it's a low-priority item for the 8700.1/8900.1, 10 years is a bit long to let a glaring error sit around uncorrected.
One anecdotal piece -I am aware of one enforcement action that was initiated against an instructor for a violation of 61.195 for giving instrument instruction in a multi with a CFI-ASE and CFI-IA but not CFI-AME (but with an AMEL on the commercial certificate). The information I have (I was not directly involved) is that after the FAA Inspector conferred with Lynch, the action was dropped.