[Phalanx]

Take care of yourself up front - so that you can better perform your job.
Distractions like this lead to further injury, and poor morale - both things that effect your work (and others) in a negative way.
I think your boss/work answered for their immediate benefit, rather than on the basis of a realistic assessment for the potential outcome.
A lot of workplaces are irresponsible when it comes to these things, not wanting to acknowledge that you've actually been injured on their watch, playing it down so people don't take further action and/or seek compensation, while not wanting to (I suppose fairly enough in some small way) increase the workload on existing staff/have to call someone in.
I take it your workplace isn't big on the whole OH&S (or equivalent) deal...if they were, they'd be the first to send you for medical help - this not only covers them having taken the correct and responsible procedure, but also ensures your injury won't get worse or infected, and that you're in the best shape you can be for future shifts...