Actually, I think your analysis is off. Their real problem, in my opinion, is that they never got their systems working smoothly.
Configuring a BB server is a bitch, and it all depends on connectivity to RIM, which is a dumbass move. Then they put out several generations of handset that failed during normal use due to design flaws, and then they rolled out BB10 which doesn't sync as well as the older system, and crippled their companion tablets in the process instead of providing the software upgrade they'd promised.
If they'd have run their corporate and consumer sides as seperate platforms, done some decent usability and QA testing, made sure their systems required only connectivity to their home server with a phone-home to RIM only to register a BBM address... they'd probably still own the corporate world. Instead, they screwed up each time they made a change - improving some things, but damaging others.
When all the employees (and, more importantly, the management) want Android/iOS, it's very, very important to keep the techies happy so we can articulate why BlackBerry is a much better choice for security, control, and TCO. We can't do that anymore, at least not strongly enough to justify sticking with the BlackBerry platform.