It depends on the size of the company. Once past a certain size, there is not much a manager, even at director level can do to give an employee a raise out of review time. The HR "partner" have a big rule book on compensation and the poor manager can only "slot" his/her reports into a predefined range. A startup does have more flexibility to adjust compensation.
HR doesn't actually run the business- they're actually there to serve the business needs.
You were 'let down easy' by whoever told you that. It's human civilization on planet Earth, everything actually is negotiable, and "my hands are tied" is just a negotiation strategy.
Yeah, as someone who has (sort of) hid behind that excuse to shift the blame, let me tell you - that's an excuse people hide behind to shift the blame. It's like 'legal won't let me'. Bullshit, you don't care about it enough to ignore the advice that legal gave you. HR's role is to serve the business, not the other way around.
