Rambam's understanding of ptil techeiles

The Rishonim debate how many strings of techeiles one is required to have in tzitzis.  Rashi and Tos hold there need to be 2 white strings and 2 techeiles strings; Raavad holds that 1 of the 4 strings must be techeiles; Rambam holds 1 of 8.  Rashi and Tos (see Menachos 38 d"h ha'techeiles" base their view on the gemara's derasha on the word "gedilim" being written in plural -- gedil = 2, gedilim= 4. They interpret this to mean not just that 4 strings are required, but that 2 of each variety are required.  Raavad's view is easy to understand -- "ptil techeiles" = 1 ptil, or 1 thread of techeiles.  The hardest position to explain is that of the Rambam.  What is the logic in requiring only 1 of 8 strings -- IOW, half of one fo the 4 whole strings -- to be techeiles?  It is not a gedil, and not even a whole ptil?

The Mishna in Menachos tells us that lavan is not m'akeiv techeiles and techeiles is not m'akev lavan.  The simple pshat in the Mishna is that if you don't have white string you can make tzitzis entirely out of techeiles string; if you don't have techeiles, you can use all white strings.  The Rambam, however, formulates the Mishna's law a little differently (Hil Tzitzis 1:4):

והתכלת אינו מעכב את הלבן והלבן אינו מעכב את התכלת. כיצד הרי שאין לו תכלת עושה לבן לבדו. וכן אם עשה לבן ותכלת ונפסק הלבן ונתמעט עד הכנף ונשאר התכלת לבדו כשר:

When it comes to techeiles not being m'akeiv, the Rambam writes, like we said above, that you can make tzitzis entirely of 4 white strings, but when Rambam quotes the din of lavan not being m'akeiv, he does **not** say you can make tzitzis out of all techeiles string.  What he says is that if you had tzitzis made with white string which then broke so that all that is left is techeiles, the tzitzis are still kosher. 

Why did the Rambam reinterpret the Mishna this way rather than read it k'peshuto?

The answer becomes clear if we look a little earlier in the same perek, to the Rambam's description of how to tie techeiles:

ענף שעושין על כנף הבגד ממין הבגד הוא הנקרא ציצית מפני שהוא דומה לציצית של ראש. שנאמר ויקחני בציצית ראשי. וזה הענף הוא הנקרא לבן מפני שאין אנו מצווין לצובעו. ואין לחוטי הענף מנין מן התורה:
ולוקחין חוט צמר שנצבע כעין הרקיע וכורכין אותו על הענף וחוט זה הוא הנקרא תכלת. ואין למנין הכריכות שכורך חוט זה שיעור מן התורה:

The Rambam in this halacha defines tzitzis as the strings attached to the corner of the garment, and then defines techeiles as the colored string wrapped around those strings.

Implicit in this halacha is a chidush: techeiles is defined not just by its color, but also by its function: it's the string you wrap around the other strings.  The Rambam must have understood that ptil is not a string, but means something wrapped. 
To make tzitzis entirely out of techeiles string would make no sense because by definition techeiles is something wrapped around other strings -- if there are no other strings to wrap around, then your techeiles is not techeiles.  Lavan is not m'akeiv if it is cut off, but it's presence is certainly m'akeiv in order to have something to wrap around.

(Why not wrap techeiles around techeiles?  It seems that techeiles would not fit the Rambam's definition of tzitzis as "min kanaf" as a garment is not usually made entirely out of techeiles.  Korach is next week's parsha -- we're not there yet : )

(See the article by R' Shabtai Rappaport on the ptil techeilet website who spells out this understanding of the Rambam).