I think it’s still important to take rest days if you’re only running, or doing minimal workouts. I’m not sure if I should be interpreting working out minimally as infrequent workouts where rest days are built in, or where you frequently do a short workout, but if it’s #2 I think you should still rest, just a little less frequently than if they were burnout workouts. Most race training plans have you run only 5 days a week at most, usually, so I think that’s a fine benchmark. You need rest to recover, without it your body can’t adapt to the stress you’re applying and make appropriate growth changes.
I also think that running on rest days is Ok, I take active rest days like that occasionally, where the workout is easy or short and I take a full rest day the next week for certain. I can’t say if this will be good for all athletes, but taking one full rest day every 14 days had worked for me. But YMMV.
I’ve definitely been talking more rest days than I want this month, and not committing to taking deload weeks seriously, but they’re important to successful growth and change.