conditions such as plantar fasciitis, achilles tendonitis, ilio-tibial band syndrome etc need to be rested/rehab'd

serious injuries such as muscle/tendon tears need rest/rehab also

minor injuries such as muscle/tendon strains can be "run through" - if I don't strain something on my serious training runs then I know I haven't been trying hard enough

obviously, the trick is knowing the difference between what will get better on a "two steps forward, one step back" basis
and what will just get worse...