I think it is true that many think of languages and words as a string of morphemes, while this notion is being challenged lately, it did have a very strong hold upon many linguists' minds. If you think about it, the further back you go, the more people relied on morphemes. A good example could be some old English dictionaries with etymology such as the one I have. Another example would be Esperanto itself, where this is a huge problem: morphemes are everything. This is one of the biggest downsides for me. Think about the "suffixes" which can equally be treated as whole words or units of meaning, it seems Zamenhof really believed in the theory of morphemes. You have for example:
malamiko "enemy" (mal- + amiko).
Note the prefix mal- which marks the opposite of something, the antonym if you will. It can be used as a word in itself, remember that it is considered still a prefix;
Other examples include:
junulo "youngster, young person" (juno + ulo, or more "natively" jun'ul'o)or;
vortaro "a group of words, dictionary" (vorto + aro, or vort'ar'o, with suffix 'ar' meaning "a group of, a collection of")
butaro "a group".
This is done in Esperanto intensively. In the same line I find in one of my dictionaries analyzing words things like a noun-forming suffix for proto-Aryan (sic) -ti, and thus giving English tru-th, divided into the morpheme of "true" and the morpheme of "noun", and other examples are presented in Latin do-ti, dowry, men-ti, mind, mor-ti, death.
The Atlantean Affair
I still remember it being mentioned that in the script the "Latin" phrase used by the protagonist (Milo Thatch) was written and analyzed as:
Dic-es lingu-as Rom-ae (sic)
To mean "you speak the language of Rome?" Jokes about how incorrect the phrasing is aside, it is plain that they mark the "morphemes" to relate them to the morphemes of Atlantean, as exemplified in the same text:
Which is, by the way, reworked into "Latin":
It-a, su-m ami-ce via-tor. (sic)
In this last one you can even detect a very big mistake. The idea was to translate "Yes, I am a friendly traveler", but the problem is that in that sentence "friendly" is an adjective, it modifies "traveler", it looks like an adverb, but it isn't. So it actually says, "Yes, I'm a traveler in a friendly way", I don't know, maybe he means he never mistreats his back-pack.
So, as you can see, so dependent were they on morphemes that they thought they could just replace the -ly morpheme for adverbs (which in English can also be used in adjectives) with the Latin morpheme -e for adverbs. And therein also rests my idea about why morphemes are not the refined tool we are lead to believe and why David Peterson is totally right, here we see that the "adverb morpheme" in fact does not act as an "adverb morpheme" but as an "adjective morpheme". There's no 1 to 1 morpheme to meaning, there's no 1 to 1 perfectly determined category for each morpheme, and even when you can work them into morphemes they will back-slap you right to your face...
Morphemes, they never fail to disappoint.