There's some truth to it, but it misses the larger context.

The decision to ease restrictions on crossings at the German border did not come out of a vacuum. It was not as though one day the East German government was just humming along as normal and then the next they decided to open up the border a little, but had miscommunicated it in a way that indicated the border was completely open. Rather, the opening was a response to tremendous pressures, and while the opening was not intended to be quite as was accidentally communicated, it's very likely that the same result would have very quickly come to pass even if it had been communicated precisely.

The '80s were a time of great change in Eastern Europe (and in the Soviet Union as well), with intense protests, strikes, and dissident organization. Two particularly noteworthy examples of this were the political victory of "Solidarity" in Poland (reaching a strong inflection point in June of 1989) and the incremental collapse of communism in Hungary throughout 1989, involving the deactivation and dismantlement of the border fence between Hungary and Austria from April through June and onwards of 1989.

The removal of the Austria-Hungary border fence in particular created a gap in the proverbial "Iron Curtain" between Eastern and Western Europe. Throughout the remainder of 1989 there was an increasing flow of East Germans fleeing the Eastern Bloc by traveling through Czechoslovakia to Hungary to Austria and then to West Germany (or elsewhere). Some made their way to Czechoslovakia and then to the West German embassy in Prague. From roughly September through October and early November hundreds upon hundreds of East Germans had fled the country in this way. In early October negotiations had allowed for thousands of East Germans who had gone to the West German embassy in Prague (and several hundred who had done the same in Warsaw) to be allowed to travel to West Germany via sealed train cars.

On November 4th over half a million East Germans filled the streets of East Berlin with a massive demonstration at Alexanderplatz in the heart of the city. Within the first week of November the government was already disintegrating. General Secretary (effective head of state) Honecker, in office since 1971, stepped down in late October. On November 7th the Prime Minister and 2/3rds of the Politburo resigned.

Also on November 7th the Politburo (or what was left of it) decided to significantly ease travel restrictions, allowing virtually anyone to apply for either permanent or temporary travel from East to West Germany even for personal reasons, and that folks who were allowed to cross could do so at any border crossing. It was intended that this new policy would go into effect the day after it was announced (the announcement being planned for Nov. 9th). However, the official who was tasked with making the announcement on the 9th was not fully briefed on all the details, and given just a short note. One of the biggest mistakes he made was saying that the new rules took effect immediately, rather than the next day. This very rapidly lead to a huge crush of folks trying to cross to West Germany, coupled with a collection of border guards who were clueless about what to do and unable to get clear instructions from East German leadership over the phone. Finally, near midnight with the crowds too large to control and no clear direction from East German officials the gates at the Bornholmer Strasse crossing were simply opened, by order of the Lt. Col. in charge (Harald Jager).

The situation remained quite "fluid" (as they say) in the immediate aftermath, but there was no way to put the genie back in the bottle. The East German leadership made what had become a de facto reality official, and opened up even more border crossings, eventually allowing for visa-free travel in late December. Initially the East German government had been trying to prevent actual damage to the border wall, but they quickly realized it was a futile effort and stopped doing so.

The effective fall of the Berlin Wall hastened the fall of Communist regimes in Eastern Europe that had already been in progress through 1989. Through November and December the communist governments of Czechoslovakia and Bulgaria fell. In the span of a single week in late December massive demonstrations in Romania transformed into riots and then fights with security forces, and then when the military changed sides the revolution rapidly took control of the country and only days later the deposed president was executed. And, of course, throughout the years that followed Communism in Eastern Europe continued to crumble (with the fall of Albania, civil war in Yugoslavia, the dissolution of the Soviet Union, etc.)

By the time of the November 9th announcement of changes to East German travel restrictions the writing was already on the wall. The limited changes they had intended to make were more aspirational than anything else, a desperate attempt to find something not quite at the level of "all the way open" that could satisfy the intense demand that had built, but in practice of course nothing short of completely opening the border would have worked. Ultimately, whether the announcement had been communicated clearly or not there likely still would have been the same intense crush of people at the border crossings, there still would have been a complete absence of clear directions on what to do about it from higher authorities (the only real options being somewhere along the lines of "shoot people until they stop crowding the border crossings" or "let everyone through"). And, of course, the end of the East German communist government was already in the wind. The Alexanderplatz demonstrations, the existing refugee flow through Czechoslovakia and Poland, the mass resignations, all of that had made the outcome ultimately clear. Nobody in the East German government in October or November of 1989 thought that they were standing on solid ground, they all understood that they were on a rapidly eroding cliff face and the question was mostly just what would come next (and whether they would survive to see it).