Interesting quote. I also doubt he wrote it. I have always doubt in that his 1917 diary, maybe someone said to him what to wrote in it, or even he heard stories about Tsarist Regime and him included, so he may wrote something he heard.
I think in his 1916 diary, some entries are very hard to understand, since, it was said sometimes he dictated, and person who wrote down lines maybe change words, and made them different from his own ones. Understand what I mean, OK?
But, his handwriting is in his diary, and even I didn't see handwriting about date you mentioned, it seems unlikely who wrote it. Right?
Even I don't know if one book/diary (same one), he used for both 1917 and 1918, or not> One which was found at Letemin's house was 1918 one, or both 1917/8? I think only his 1918 volume.