Schach Pasul of 4 Tefachim

ז] נְסָרִים שְׁאֵין בְּרָחְבָּן אַרְבָּעָה טְפָחִים, מְסַכְּכִין בָּהֶן אַף עַל פִּי שְׁהֶן מְשֻׁפִּין; וְאִם יֵשׁ בְּרָחְבָּן אַרְבָּעָה, אֵין מְסַכְּכִין בָּהֶן וְאַף עַל פִּי שְׁאֵינָם מְשֻׁפִּין--גְּזֵרָה שֶׁמֶּא יֵשֵׁב תַּחַת תַּקְרָה, וִידַמֶּה שְׁהִיא כַּסֻּכָּה. נָתַן עָלֶיהָ נֶסֶר אֶחָד שֶׁיֵּשׁ בְּרָחְבּוֹ אַרְבָּעָה טְפָחִים--כְּשֵׁרָה, וְאֵין יְשֵׁנִין תַּחְתָּיו; וְהַיָּשֵׁן תַּחְתָּיו, לֹא יָצָא יְדֵי חוֹבָתוֹ

The Rambam here is saying that in general boards of wood that are 4 tefachim wide are pasul as schach because of a gezairah that someone will then think that a regular roof is good as a sukkah. This halacha is based on an explicit gemara in sukkah. The next part of the Rambam, however, is difficult.

The Rambam says that if one used one board of wood 4 tefachim wide the succah itself is kosher. However, one may not sleep under that particular board, and if you do you aren't not yotzei. The difficulty here is from the following Rambam, also based on a gemara:

בְּסֻכָּה גְּדוֹלָה, סְכָךְ פָּסוּל בָּאֶמְצָע--פּוֹסֵל בְּאַרְבָּעָה טְפָחִים, פָּחוּת מִכָּאן כְּשֵׁרָה; וּמִן הַצַּד--פּוֹסֵל בְּאַרְבַּע אַמּוֹת, וּפָחוּת מִכָּאן כְּשֵׁרָה

Here the Rambam says that if one has schach pasul (e.g. metal rods) of 4 tefachim in the middle of the sukkah the entire succah is pasul. Only if the 4 tefachim are on the side of the sukkah is the sukkah kosher because then we can employ the rule of dofen akumah. One may, perhaps, suggest that the earlier Rambam we quoted is only talking about when the 4 tefachim board of wood is on the side of the succah. Some, I believe, do suggest this. However, this answer is a dochek. The pashtus is that the earlier Rambam was talking about where the 4 tefachim board of wood is in the middle of the sukkah and still the entire succah is not pasuled. The question is, what is the difference between 4 tefachim of schach pasul in the middle of the succah and a 4 tefach board of wood in the middle of the succah?

Update -the answer: I think that really the only way to go here is to say that when the chachamim invalidated a board of wood 4 tefachim wide it did not have the exact same status as actual schach pasul. The question is exactly how to define this distinction. The way I thought to explain was as follows:
Schach pasul has a challos shem in it that it is just that - schach pasul. It is a challos in the cheftza of the schach. However, by a neser of 4 tefachim the chachamim never assured the board in the cheftza, i.e. they never said that the board of wood has a challos shem of schach pasul, rather it is just assur to be used as schach.
You may ask: what in the world is the difference? In either case, it is assur to use the board of wood as schach! What difference does it make if there is a challos in the cheftza or not?
The answer is the same anytime there is a gavra/cheftza chakira. If something is assur in the cheftza than other "satellite" dinim will be affected. We know that schach pasul is assur to be used as schach. This is obvious. However, there is another area of halacha that schach pasul can affect. That is, of course, the ability for schach posul to pasul the rest of the succah. This din is dependant exclusively on the fact that the schach pasul has a challos shem in the cheftza of schach pasul. Why is this so? That issue gets into the lomdus of why it is that schach posul of 4 tefachim passuls the entire succah at all. In the future, I hope to iy"h get into this issue but it really involves the gemaras as well. (Asher M. in the comments already stated the main idea with regards to this issue, namely that 4 tefachim of schach posul passuls by "dividing" the succah in half and that a board of 4 tefachim doesn't act as a "divider". But, as I said, this issue gets more involved with the gemaras, so we'll leave it off for now.)