I don't think you HAVE to eat them together. I think the advice is usually given to people who are supplementing iron. Take the iron pill with a glass of OJ.
The other advice I've heard is not to take your iron supplement within a couple of hours of a cup of coffee.
It could be a logical fallacy on my part but I'm thinking if coffee inhibits iron absorption for hours, then vitamin C would improve absorption for a couple of hours.
When I give blood they check my iron levels. I am almost always borderline anemic. increasing my iron intake with foods helps the most. Strangely, eating a bag of apricots during the week before the test helps a lot. I have taken a supplement and found that i can't stand more than about 50% of the RDA. if your stools turn black and become rock hard you are ingesting more iron than your body can absorb. I selected my multi with iron partially because it only has 33% of the RDA of iron.
A lot of good healthy vegan foods ARE high in iron. but the non-heme iron found in plant foods IS not as absorbable as heme iron. So the vitamin c and coffee timings are probably really important. If you monitor your iron intake with something like Cronometer you should probably shoot for a number over 100%.