Just curious here, which vote percentages are you referring to? Because even a quick google search on the results brings up the wikipage on the referendum and the only ones where you have "over 99% of the people agreeing" on the referendum were the unofficial polls in places like Georgia, where it was only held in Abkhazia and South Ossetia (both places where the non-Georgians had an interest in remaining in some sort of union with Russia), and Lithuania (where it was likely held among only the population of East Slav migrants into the republic).
The rest of the results generally range from 70-80% support in the East Slav republics (Russia, Ukraine and Belarus) with turnouts of 75-80% (so total active support being somewhere between 52-64% of the registered voters) to 94-98% in the Central Asian and Caucasus republics (Azerbaijan, Kazakhstan, Uzbekistan, Tajikstan, Turkmenistan and Kyrgyzstan) with turnouts of 75-99% (so total active support being somewhere between 70-97% of the registered voters).
I wouldn't be very quick to dismiss the nature of the vote in the Central Asia and Azerbaijan though since:
1. if it was being rigged, why bother allowing some republics (Estonia, Latvia, Lithuania, Georgia, Moldova and Armenia) to boycott it?
2. Even up to 2006-2008, a well reputed western polling agency (Gallup) found 40-50% of respondents in Kyrgyzstan, Kazakhstan, Uzbekistan and Tajikistan favoured the idea of the CIS becoming either a "one country" or a "federal state" (I provide links to the polls as well as the poll results and more discussion on them
here). The support in Russia for the same question was around 42% and was in general lower than in Central Asia (excepting Kazakhstan). If 15 years after the referendum, support in Central Asia was broadly higher for having the former USSR re-made as a federation or possibly even unitary state (!), then it seems believable that the support would be higher in Central Asia than in Russia, Ukraine and Belarus for the continuation of the federation of the USSR in the 1991. If we take the actual difference to have been 10% greater support then
even if there was rigging, the unrigged vote might well have been somewhere between 80-90% of the raw vote and 60-70% of the total registered voters (which is only about 10-20% more than in the Gallup poll of 15 years later anyway).
3. The rule of thumb that a 99% vote (or something similar) is generally rigged isn't that rigid as there have been a number of exceptions over the years: The
Dominican Republic in 1870 (99.93% in favour of annexation to the United States although with a 30% turnout),
Norway in 1905 (99.95% voting in favour of independence from the union with Sweden with an 85.4% turnout),
Iceland in 1918 (with 92.6% in favour of the new personal union with Denmark, although with only a 43.8% turnout),
Iceland again in 1944 (99.5% in favour of independence/abolishing the union with Denmark with a 98.4% turnout and 98.5% in favour of the proposed constitution with the same 98.4% turnout),
Gibraltar in 1967 (99.64% voted in favour of continued ties to the UK with a 95.67% turnout),
Djibouti in 1977 (99.8% in favour of independence with a 77.2% turnout),
Armenia in 1991 ( 99.5% in favour of independence with a 95% turnout),
Lithuania in 1991 (93.2% in favour of independence with a 74.9% turnout),
Macedonia in 1991 (96.4% in favour of independence with a 75.7% turnout),
Croatia in 1991 (93.24% in favour of independence with a 83.56% turnout),
Turkmenistan in 1991 (94.06% in favour of independence with a 97.4% turnout) and
Uzbekistan in 1991 (98.3% in favour of independence with a 94.1% turnout),
Georgia in 1991 (99.5% in favour of independence with a 90.6% turnout),
Azerbaijan in 1991 (99.8% in favour of independence with a 95% turnout),
Gibraltar again in 2002 (98.48% reject shared sovereignty with Spain in favour of the status quo with an 87.9% turnout),
South Sudan in 2011 (98.83% in favour of independence with a 97.58% turnout), and the
Falkland Islands in 2013 (99.8% vote for continued British rule with a 91.94% turnout).
Even if one wanted to discount the various referenda in the Soviet and Yugoslav states, the others demonstrate that a poll with an incredibly high turnout and 90% or more support in favour of a poll option does not have to be rigged. And that over 90% of a population can actively vote for independence wouldn't mean it was impossible for over 90% of a population to vote for unification or continued unification.