Some of R’ Elchanan’s proofs that takkanos derabbanan are not rooted in a pasuk but are rooted in Chazal’s ability to intuit or interpret the ratzon Hashem:
1) Takanos existed before matan Torah introduced “lo tasur”. One example is Moshe interpreting Hashem’s command to include an extra day of preparation before mattan Torah (“hosif yom echad m’da’ato”). The license to interpret Hashem’s command preceded any formal granting of authority to do so. We also find various references in Midrashim to takanos of Shem v’Eiver.
2) The Rambam (Hil Shabbos ch 24) writes that Chazal instituted the laws of muktza to limit weekday activities and enforce the idea of Shabbos as a day of rest, as taught in the pasuk “l’ma’an yanuach”. Someone who violates a law of muktza is certainly not guilty of violating a Biblical commandment of “l’ma’an yanuach”. The commandment is not the source for the specific laws of muktza, but is the source for the fact that G-d desires Shabbos to be a day of rest, which in turn is the impetus behind the Rabbinic muktza laws.
3) R’ Elchanan presents an interesting spin on the Bila’am story. Since G-d did not explictely tell Bila’am not to go with Balak (see the meforshim who offer various suggestions on how to read Hashem’s warning to Bila’am so that it was not an explicit command), why is Bila’am blamed for acting based on his own desire? R’ Elchanan answers that it is not the command of G-d alone which we should heed, but G-d’s will. Since Bila’am recognized G-d’s desire to protect the Jewish people, even sans an explicit command not to harm them he should not have gone with Balak. What comes out of this discussion is a powerful moral lesson: a legal technocrat may skirt the law by taking advantage of existing loopholes, but the goal of halacha is not simply obedience to technical statutes but obedience to G-d’s will.
The Nesivos famously writes that an issur derabbanan violated b’shogeg requires no kaparah because the entire basis for dinim derabannan is to prevent a rebellion against the authority of Chazal – “lo tasur”; an act done b’shogeg cannot be called a rebellious act. However, according to R’ Elchanan’s thesis, Chazal’s role is to reveal the ratzon Hashem; the reason for obedience is not just to respect their authority, but because the laws they enact reflect what is inherently right/wrong. Lack of intention to disobey common sense does not preclude getting burned while touching a hot stove. Similarly, lack of intention when violating a din derabbanan may not preclude the need for kaparah for performing that which is wrong. (My son asked me over Shabbos based on a shiur he attends whether eating an issur derabbanan b’shogeg is metamtem halev. Perhaps the question hinges on this issue).