Obama wasn't allowed to keep his Blackberry; he requested a secure commercial-quality cellphone to communicate with his aides, and NSA (which was, to be sure, not really happy about the request) selected the Blackberry as their platform. The end solution was a highly pared-down device that could only communicate via a hosted encryption server (a commercial product, SecurVoice) to a small number of paired devices, which were distributed to Obama's inner circle. The Presidential devices had additional security limitations (e.g., they could only connect to WHCA-controlled base stations). End of the day, what they had was an encrypted closed network of devices, some of which communicated over public wireless infra, running a very limited, NSA-reviewed, approved, and altered, software suite.
What's clear is that NSA put a fair amount of effort into securing and maintaining that system, so much that its use was limited to the White House; Hillary Clinton wanted a similar setup (her predecessor, Condoleezza Rice, had been allowed to use unaltered "off the shelf" Blackberries under an NSA waiver, but NSA had declined to renew those waivers due to security concerns), but NSA slow-walked and effectively derailed the discussions with State's security team, perhaps because they wanted to limit the amount of technical detail discussed outside the White House, or because they were concerned that State would be unable to provide SecState with the kind of technical support necessary to secure the devices during global travel. (We all know what happened next, of course.)
What's clear is that NSA put a fair amount of effort into securing and maintaining that system, so much that its use was limited to the White House; Hillary Clinton wanted a similar setup (her predecessor, Condoleezza Rice, had been allowed to use unaltered "off the shelf" Blackberries under an NSA waiver, but NSA had declined to renew those waivers due to security concerns), but NSA slow-walked and effectively derailed the discussions with State's security team, perhaps because they wanted to limit the amount of technical detail discussed outside the White House, or because they were concerned that State would be unable to provide SecState with the kind of technical support necessary to secure the devices during global travel. (We all know what happened next, of course.)