... I bring this up because I’ve recently heard several people tell me something along the lines of “Well, if my company wants me to learn new technology, they’ll need to tell me what to learn, pay for it, and give me the time to learn it.†...
Regardless of industry, successful people do whatever it takes to master their profession. In a nutshell, that (even more than raw talent and opportunity) is what separates winners from losers. I'll confess upfront that I'd continue spending a significant portion of my day learning... even if my employer explicitly directed me not to. Were I to get fired for my insubordinate learning, I'd just find another job to learn with. I honestly don't know how to stop learning.
Agreed. If an organization tries to stop you from learning (let alone won't support you), it's not a place I'd care to stay at.