(I found myself using "African" to mean native-origin black people, as in Rhodesian law, but sometimes "white" where it sometimes used "European", which in law meant "not African". I mean no offense or confusion.)

The Story So Far, Like the Intro Scroll in The Phantom Menace

Rhodesia had been a UK settler colony, in which there was complete dominance by the 6% of the population who were European. With decolonialization going on, the UK insisted on "No independence before majority rule" (NIBMAR), and five principles of independence for Rhodesia. They are on p. 3 of Chengetai J. Zvobgo, "Church and State in Rhodesia: From the Unilateral Declaration of Independence to the Pearce Commission, 1965-72", Journal of Southern African Studies, Vol. 31, No. 2 (Jun., 2005), pp. 381-402, http://www.jstor.org/stable/25065000.

The white government of Rhodesia refused, did not agree with the UK in negotiations, and then issued a Unilateral Declaration of Independence (UDI) on 11 November 1965. The UK's government, and the UN, US, and all other nations, refused to accept it, and enacted sanctions.

In the early 1970s, the new Conservative government of the UK was looking for a way to break the impasse (partially pressured by internal rebels, partially from the outside). The UK's government and the Rhodesian (white) government negotiated an agreement that was purported to meet the five principles. The Rhodesian government agreed to certain provisions, and the UK would recognize Rhodesian independence and drop sanctions.

A summary of the proposals and the general area is at Alvin Madzivanzira, "The Pearce Commission 1972", The Patriot, 28 August 2014. I gather that the source is strongly ZANU–PF, but it appears to be a fair summary of the Proposals. The full proposals can be seen in UNITED KINGDOM: PROPOSALS FOR A RHODESIAN SETTLEMENT, International Legal Materials, Vol. 11, No. 1 (JANUARY 1972), pp. 185-205, Cambridge University Press, http://www.jstor.org/stable/20690859.

Principle #5 was "The British Government would need to be satisfied that any basis proposed for independence was acceptable to the people of Rhodesia as a whole", meaning "including Africans". No Africans had been in the negotiations, few Africans were in the Rhodesian parliament (roughly 9% of the lower house), and some of those few were there because of co-opted leaders. The UK insisted on sending to Rhodesia a commission, led by Lord Pearce.

(edit: Lord Pearce was a bit more important than I had thought. As I mention in replies below, he was a retired "Supreme Court" judge and I suggest reasons why he in particular was chosen.)

The first difficult question of how they could find out whether it was "acceptable to the people of Rhodesia as a whole" when there was no mechanism of voting, existing restrictions on rural African political meetings, and dozens of political prisoners (including a former Prime Minister). And Rhodesian Prime Minister Smith's government was insisting that Africans had no notion of voting, that there was a "silent majority", that they were the "happiest Africans in the world", that "that there was too much intimidation for the test to yield reliable results, that tribal Africans always shouted 'no' to ideas they did not wholeheartedly support" (paraphrased by Luise White, "'Normal Political Activities': Rhodesia, The Pearce Commission, And The African National Council", The Journal of African History, Vol. 52, No. 3 (2011), pp. 321-340, http://www.jstor.org/stable/41480243). And Smith later condemned the commission because "they carried this out on the basis of one man one vote, as if they were counting sheep" ("Church and State in Rhodesia"), the monsters.

The eventual method was largely to have public meetings in the presence of chiefs. The Commissioners found them "'boisterous' but 'friendly and good-natured if sometimes noisy'", never felt threatened in general, and believed that the meetings did not display sullenness that might betoken intimidation (ibid). There were allegations of bribery pro and intimidation con. And as the report itself said, "We found it improbable if not impossible that with such a tight security system as that which has existed in Rhodesia for several years, a minority could dominate a majority by intimidation in a few weeks ..."

OP's Actual Question, "why was the answer no?"

Under such conditions, there could be no definite determination of the exact reasons. The Pearce Commission reached some conclusions, though.

"reading the writeup from the Pearce Commission" shows a lot more patience in getting Inter-Library Loan, and determination in reading a 207-page government report, than I had! Rhodesia: report of the Commission on Rhodesian Opinion under the chairmanship of the right honourable Lord Pearce, presented to Parliament by the Secretary of State for Foreign and Commonwealth Affairs, London, H.M.S.O., 1972.

I'm going by the verbatim quotations in "Church and State in Rhodesia". The which verbatim quotations from the report answer the question.

The bedrock reason was that the Africans had absolutely zero trust in Smith, his government, the white apparatus, and the whites generally. To state why the Africans said "no", I can do no better than to quote the Pearce Commission's report, quoted in "Church and State in Rhodesia". Pp. 80-81:

Mistrust of the intentions and motives of the Government transcended all other considerations.... One [African] summed it up in saying 'We do not reject the Proposals, we reject the Government'. This was the dominant motivation of African rejection at all levels and in all areas. Few could bring themselves to believe that the Government had changed its policies or that the European electorate on whom it depended was prepared to change its attitudes or its way of life. Most refused to see advantages in the Proposals. Those who did doubted whether the Government would ever implement them. These people thought that as soon as Independence was recognised and sanctions revoked, a Government which had torn up previous constitutions could do so again; and even if the Government kept faith, the white electorate would turn them out and replace them by representatives and parties not committed to the present terms. A majority of Africans were convinced that the present governing party was committed to the perpetuation of white supremacy in Rhodesia. They argued that the Government had not sought the support of the African in the past, and were not likely to do so now.

Another, almost as fundamental, objection was that no Africans had been involved in it. The United Methodist Church in Rhodesia called it "a deal between white people by white people for white people". P. 82:

Many criticised the lack of effective consultation with African leaders. No Africans had been involved in the negotiations; they were therefore not a party to them. If their national leaders had been involved and said they should accept, that would have been different. Some said that for this reason earlier British proposals would also have been unacceptable to Africans. It was also argued that the issue was essentially one between the Europeans and Africans in Rhodesia, or between the Rhodesian Government and the Africans; it was not between the British and Rhodesian Governments; it had to be settled in Rhodesia. Because no African was present or consulted some suspected that the present agreement was designed to benefit the European but not the African. Some thought that better terms could have been obtained if Africans had been present; others believed that there was something to hide. All who raised this point asserted that the African had a right to be consulted and that neither Government appreciated African aspirations; Africans should no longer be thought to be incapable of expressing their own needs.

Huh, I've never gotten "this is too long (max: 10000)" before. To be continued about the specific proposals.