What specifically about the text are you wondering about?
Yes, it is true Gorbachev proposed complete nuclear disarmament to Reagan.
No, it is not true Reagan brought down the Soviet Union by uttering two words. It was actually Chuck Norris.
"It was exactly the opposite of the nuclear arms race in the 40s and 50s, in which the US worked like crazy to develop massive offensive weapons which it jealously guarded."
This is debatable. The US attitude towards nuclear proliferation before Kennedy took office was a mixed bag. During the Eisenhower Administration, numerous US officials, mostly at the State Department, actually pushed for giving the nuclear options to West Germany and especially Japan. However this started to change after Ike went on a tour of NATO facilities in Europe and the Middle East and was "enraged" discovering nuclear armed F84 fighter bombers belonging to the West German and Turkish air forces were on a 24 hours alert. What enraged Ike so much is the fact the weapons came from US stocks and the famous "dual key agreement" was sloppily implemented at best, meaning West Germany and Turkey had the potential of using nuclear weapons without prior US authorization.
"Reagan, on the other hand, saw SDI as the way forward into a post-nuclear era."
The man we'd really need to talk to about the SDI is Caspar Weinberger, Reagan's powerful Secretary of Defense. According to an historian Weinberger "had never seen a defense system he didn't like". To this day is debated whatever Weinberger was just a shill for the military-industrial complex or, in accord with other government officials including Reagan himself, he willingly stepped on the military spending pedal to "spend the USSR into oblivion". The truth probably lays somewhere in between.
"Gorbachev reiterated his point that SDI was destabilizing. Reagan reiterated his point that it wouldn't be, because the US would share every scrap of the thing. Gorbachev dismissed this on the ground that just a few months before, the US and USSR diplomatic corps had failed to reach a mutual agreement on the technological exchange of milking machines. Seriously. Like, for cows. If you won't give us your milking machine technology, Gorbachev said, why should I believe you'd give us the ultimate space weapon?"
Again this is open to debate. The US approach of sharing sensitive technology with foreign countries (regardless of them being allies, neutral or foe) changed radically in the second half of the '70s. During the buildup to the Yom Kippur War, the Shin Beth (Israel's shadowy internal intelligence agency) started tracing encrypted communications originating from Israel and directed to the KGB's post in Cyprus. Thanks to a genius linguist they were able to crack the code open and discover the content of this stream of communication. However, due to the sophistication of the encryption they were never able to discover the source of the signal. A little before the 1979 Revolution, a joint CIA-SAVAK (the Shah's feared secret police) operation netted a KGB agent in the upper levels of Iranian administration. He was found to be in possession of a US-made communication device of the type issued by CIA to its own operatives in the Soviet Bloc: it was the same technology that had been driving the Israelis mad. This led to a complete review of security procedures and technology sharing: it was suspected the Soviet got the devices through the British intelligence (which both the CIA and the Israelis believed to have been heavily infiltrated by KGB operatives: they were proven to be right just a few years later). If the US could not trust their closest ally of fifty years, whom could they trust? I doubt American goverment officials, who had gone to incredible lengths to keep the astounding resolution their KH-11 spy satellite was capable of secret (only Israel had access to the images, and until 1980 or so they only got lower resolution pictures), would have been ready and willing to share such advanced technology with anyone.
Another little known fact is, while many Soviet officials saw the SDI as a threat to MAD, others (especially in the KGB) saw it as an opportunity. As we all know the SDI was aimed at protecting the Continental US, leaving Europe open to a Soviet nuclear strike. Soviet diplomacy played this up to bring about a rift between European countries (many of which deeply already resented the presence of IRBM's on their soil) and the US. European Communist and Socialist Parties (all deeply influenced by Moscow) were among the most vocal critics of the SDI. That's the reason why the Bush II Administration, after resurrecting the SDI's rotten corpse, immediately "offered" European allies SDI coverage in form of early warning radars, land based interceptors and naval based missiles. It was one of the triumphs of the Bush Administration, except for Russia (they know very well who the SDI is really aimed to), no objection was raised this time around, despite the fact the systems appears to be years from being remotely effective.
Marko:Yes, it is true Gorbachev proposed complete nuclear disarmament to Reagan.
Khrushchev also proposed complete nuclear disarmament to Kennedy (source).
The keyboard is mightier than the gun.
Non parit potestas ipsius auctoritatem.