Birchos Krias Shma

Rashi on daf 2a in Berachos writes that if one says shma early (before nightfall), he is yotzei his chiyuv of shma with his krias shma al hamitah with the first parsha of shma alone. Tosafos asks, if this is the case he should need to recite all 3 parshiyos during krias shma al hamita?

I saw in the Iggros HaGrid Hilchos Shavuos 1:13 the following answer:

Rashi's opinion is that even though the zman of shma itself is from tzeis, nevertheless the zman of Birchos Krias Shma is from Plag HaMincha. Rashi can hold this because he holds that the brachos of shma are not birchas hamitzvos. Rather they are just shevach v'hodaah. Rashi, therefore holds that the zman for the brachos is actually determined not by the zman of shma itself, but by the zman of tefillah. This is based on the halacha of smichas geulah l'tfillah. Since the brachos are "geulah" there zman is defined by tefillah.

Rashi therefore holds that the second two parshiyos of shma, which are only midrabbanan, the takana was to say them as one kiyum with the brachos of shma. It is only the first parsha, which is shma d'orayssa, that has its zman defined by nightfall.