1) One cannot say that this statement is only in relation to holidays, because if we look at the Masores ha'Shas here we notice that this statement also occurs in Yevamos 85b. There the Gemara discusses various forbidden marriages and the question is, does the husband have to pay his wife's Kesuvah? The Gemara states that if the marriage was forbidden mid'Oraisa, he does have to pay but if it was only forbidden mid'Rabanan he does not pay. The Gemara gives the same reason for this as it gives in Ta'anis: Divrei Torah Ein Tzerichin Chizuk, while Divrei Sofrim Tzerichin Chizuk. So we learn that this rule does not only apply for holidays.

2) Therefore, we must say that "Divrei Torah Ein Tzerichin Chizuk" is a rule that is stated relative to Rabbinical prohibitions. The idea is that if something is forbidden at a more stringent level of prohibition, then it is not necessary to make a Siyag to protect the Mitzvah, because people are anyway more careful not to transgress it precisely because of its severity. In contrast, if a prohibition is lighter, this tempts people to be less particular about it, and therefore it was more necessary for Chazal to make a fence round it.

3) Accordingly, in Yevamos, if a marriage is forbidden only mid'Rabanan, the woman might be more easily tempted to transgress, so it was necessary for Chazal to penalize her by making her lose her Kesuvah.

Back to the Gemara in Ta'anis: Chazal were trying to protect the festive days mentioned in Megilas Ta'anis and ensure that people would not come to fast or eulogize on these dates. There was more worry that people might make light of these days because their prohibtion is only d'Rabanan and is lighter. In contrast, Chazal were not so concerned that people would fast or eulogize on Rosh Chodesh, because everyone knows that Rosh Chodesh is d'Oraisa. Therefore, they enacted only an Isur against fasting on the day before Rosh Chodesh but not on the day afterwards, because people are naturally more afraid of desecrating Rosh Chodesh so it does not need so much protection. The days mentioned in Megilas Ta'anis are only of a d'Rabanan status, and thus people take them less seriously, so Chazal enacted that one may not fast even on the following day, to stress that the day before was an important holiday.

4) In summary, certainly there are many Rabbinic decrees to strengthen observance of Torah laws. However, Chazal did not always make Gezeiros around Torah laws. Our Gemara is saying that sometimes, even though Chazal did not see it necessary to protect the Torah law, they still found it necessary to strengthen the Rabbinical law, because otherwise people might not treat the Rabbincal laws seriously.

Kol Tuv,

Dovid Bloom