Rav Yehuda said in the name of Shmuel that in 3 things the Rabanan deviated from the truth. Masechte, Bed, and hospitality.
1. Why don't the Rabanan just ignore the question of Bed and avoid telling an untruth. Must every question be answered?
Mar Zutra continues further and says that for practical purposes if we know that one deviates from the truth in an additional matter, besides these 3, then he is not believed Betvias Ayin.
2. Is it not true that a person can deviate from telling the truth when it comes to Shalom as well?
Kol Tuv,
Alex Lebovits
The thrust of your first question seems to point to Rashi's explanation, which Tosfos already rejects. Tosfos' reason may well be different than yours, but it is similar in that it is based on the fact that there are certain things that one just does not mention (the questioner according to Tosfos; the man himself, according to you).
According to Tosfos interpretation of 'Puryah', the person is simply giving a reason for not having attended the Beis ha'Medrash the previous day, in which case, your question is not really relevant.
Tosfos also asks your second question too. They answer that all three cases fall under the category of Darchei Shalom, and the Gemara only cites them because they are common.
The Rif (cited in Bi'urei ha'Daf) disagrees. In his opinion, Darchei Shalom is an independent Mitzvah, and the Gemara declines to include it in the list, because it is a Mitzvah, whereas the list comprises only items that are Reshus (voluntary).
b'Virchas Kol Tuv,
Eliezer Chrysler