I read and heared and saw it so often since the mid-90s (I was still at university) and at times when I even did not had internet. Confirmations have been given by the Fnech and the russians before, both officials and pirvate professionals like historians, editors, etc. Former czhancellor Helmut Schnidt also confirmed it, as have adivisors and people in the surrounding of the Kohl government.
Note that it is said that only Thather behaved stubbornly against it for longer time, 2-3 konths or so, but was pretty much isolated in her own government. Washington on the other hand was, like EVERYBODY, against reunificationb, and I know since the 90s that5 they also asked the Russians, like Thather, to prevent reunfication be sending in troops. However - and this part you may not ignore - events overrolled everybody, and Russia from the very beginning (Gorbatchev), France and America short time later, and last Britain understood the signs of changing times and gave official acceptance of what already was fact in reality - the wall was broken down, and the iron curtain was no longer a curtain at all.
All major nations did not want a united germany, bot after WWI, the story of Nazi-Ger,any coming back in the second half, and then WWII. Evberybody had settled down in the cold war, and made himself a comfortable nest in his corner of the mutual arrangement between West and East. It was stable. The Germans were tamed. Why messing things up again when it worked so wonderful? The talking about how uch one suzpported reunification in the future was just the kind of talking polticoians do: pathetic, bombastic, emotional, and not meant real. It was to please the crowd in the street, so that they kept smiling, calm and under control. Reunification was meant to come, sure. At some unspecific, far far away in the future. The longer the better for the status quo. The status quo was what was wanted. Even Gorbatchev has just admitted in that loinked interview he did not want Germany to reunite. He just rejected the means to achieve that from the very beginning while the three Wetsern powers wehre openly asking Moscow to send troops to keep the status quo.
As I said somewhere above, maybe it was jst the sheer pace by which events unfolded that made sure reunification was already unstoppable when wetsenr powers still had doubts on whether or not to accept a united Germany in the heart of europe again. And thank God, different to Thatcher who met Kohl with icecold and unhidden hostility in public comments, France and America came back to their senses within a short time, less than a month, if I recall it correctly.
That were the days before the internet.