The Gemara in Menachos (65b) learns from the words "U'sefartem lochem" that each individual is obligated to count the Omer for himself.
Tosfos there explains that the Gemara learns it from the fact that "U'sefartem lochem" is written in the plural, as opposed to the singular "Vesofarto l'cho" - used by the Torah in Parshas B'har, in connection with the Sh'mitah and the Yovel, and which is therefore confined to the Beis-Din.
The Torah Temimah cites the Magen Avraham (in Si'man 489), who rules that the obligation of each individual to count the Omer precludes the possibility of appointing a Shali'ach to count on one's behalf (provided one hears the counting and answers 'Amen'). And he draws a distinction between Sefiras ha'Omer and Kidush (for example), which one is permitted to be Yotzei through a Shali'ach, based on the above Pasuk, which clearly renders Sefiras ha'Omer an exception, which must be counted personally, and not through a Shali'ach.
But clearly, asks the Torah Temimah, the above-mentioned Gemara is coming to preclude Beis-Din counting on behalf of the people, as we explained, and not counting through a Shali'ach.
His question is based on the premise that we never learn two things from the same word. Consequently, seeing as the Gemara learns from the word "lachem" that one cannot rely on Beis-Din, one cannot also learn from it that one cannot rely on a Shali'ach.
