Can the above statement really be true? First of all, the common statement: "more people are alive today than have ever lived" is false. According to wolfram alpha, there have been about 100 billion people ever.
There is a possibility that we are are reaching older ages with the technology available to us today, and therefore the statement might be "more" true. I wouldn't discredit it right away, but I think it might be a little bit exaggerated, given facts such as:
In the United States the proportion of people aged 65 or older increased from 4% in 1900 to about 12% in 2000. [Citation] And in the entire world we are sitting at ~ 7.9% of 65 and older currently. So this would mean we have about 550 million seniors. This would require that out of the other 100 billion people who are not living anymore, only 250 million of them could have reached age 65. While this seems small, we have to look at what life expectancy has been historically. Curves of life expectancy in the past have looked like this:
The life expectancy curve is essentially unchanging, until the development of science and technology, and then it explodes. This gives more possibility to the "0.25% chance of reaching age 65" that is a requirement for the 2/3 statement. So as a whole, it may be viable but I would probably feel more comfortable with a statement such as "Most likely, 1/3 of the people who have reached 65 are alive today."
Finally, it is important to note that huge infant mortality rates were a large part of low life expectancy in the past. There is an interactive graph that showed age breakdown for each year, here. This graph represents some amusing data points, such as the claim that it’s impossible to die between the ages of 20 and 26.