They have been proven resoundingly wrong. While there remain questions over Facebook's other two major acquisitions, the US$19b takeover of WhatsApp and the US$2b purchase of virtual reality start-up Oculus, Instagram can count as nothing less than a triumph. The app is growing faster than Facebook itself, having signed up 200 million new users in the last nine months, and is contributing handsome sums to Facebook's top line.
Worldwide, it is expected to pull in US$8.1b in advertising revenue this year, almost double a year ago, according to estimates from eMarketer. By 2020, this will have doubled again, to US$17b.
But the app has been more than a mere financial success. It has also been a foil for Facebook when the wider company has been hit with crisis.
Instagram has largely been free of many of the controversies that have racked Facebook. Its highly visual nature, largely focused on photos and videos, means fake news has not taken hold. Its lack of sharing features means posts do not go viral.
Although users' Instagram accounts are connected to Facebook, it is the Facebook side of the business that has been seen as the ruthless data harvester.
The apps themselves have different branding, colour schemes and designs, which keeps them separate in consumers' minds.
As teenagers and young users reportedly flee from Facebook, growing disenchanted as their older relatives come online and spoil the fun, they have flocked to Instagram.
According to Pew Research, just 51 per cent of Americans between 13 and 17 use Facebook, down from 71 per cent three years ago. In comparison, 72 per cent are on Instagram. But Zuckerberg has by no means left it alone. Two years ago, Instagram introduced a feature allowing users to post photos that automatically disappeared after 24 hours. The service was unforgivingly copied from rival app Snapchat. Even the name - Stories - was the same. Eight months on, the number of people using Instagram Stories had surpassed Snapchat's entire user base.
This week, Instagram was roped in to a new challenge. It launched a separate video app, Instagram TV, designed to dethrone YouTube. The service will allow celebrities to post videos of up to an hour.
If Instagram is to succeed here, it will be through its differences with Facebook, not its similarities.