This is as true as saying that the automobile let you do what a horse could do, only easier and faster.
On the surface, it's seemingly true, but in reality the details make all the difference. Affordability, for example. Horses were expensive, not everyone owned them, whereas cars could be subject to manufacturing efficiencies and eventually became cheap enough to allow mass ownership. Also, the convenience and inexpensiveness of taking a long trip by car utterly transformed the world.
Similarly, the world is growing far more connected through the internet than it ever was via phone, fax, telex, etc. Speaking personally, prior to the internet I didn't have a lot of interaction with people living outside of my hometown, but today it's not unusual for me to communicate with friends living all over North America and Australia and to talk with acquaintances and strangers all over the world.
Also, people are not working in the same patterns. A significant number of people who do knowledge work have gone to work for themselves, which would not have been so easy pre-internet. Similarly, through inventions like ebay, etsy, crowd funding, self-publishing of music and books, and so forth a lot of people are finding it easier to switch to creative careers. How many lives have been changed by people changing their careers through sites like kickstarter and indiegogo? What percentage does that represent of all people who have made similar changes to their lives enabled by the internet and modern technology?