Does honey always have to be heated in order to liquefy it for bottling?
Knowing small-scale beekeepers personally, I can confirm that fresh honey straight from the combs is liquid(-ish) and can be put into jars directly.

I have seen (and participated) in the process of manual extraction: The full combs are uncapped (the wax lids of the cells are removed), then go into the extractor - think of an old-fashioned laundry spinner - and the centrifugal force extracts the honey. If the beekeeper did everything right, the honey can go straight into the jars, no heating or warming required.

But of course I wrote „if“.

Raw honey will crystallize at some point and yes, this may even happen while the honey is still in the combs. (But rarely, because it would mean the beekeeper has waited way too long to harvest, e.g. until spring.) Likewise, harvested honey will crystallize during storage and so the producers may have to gently warm the honey if they didn’t bottle it immediately. The speed of crystallization depends on the environmental conditions, but also on the ratio of glucose to fructose. Some types of honey will hardly ever crystallize (chestnut, for example), others will solidify almost immediately, like rape. 

(And there is also the honey that is sold in the convenient squeeze bottles: It’s often warmed beyond 70C and filtered at some point to prevent future crystallization that would clog the nozzle.)

So the short answer:
No, honey need not be warmed if it’s bottled straight from the extractor. But it may be more practical or economic for producers to do so.

You might want to note that the bees keep the temperature in the hive between 33 and 36C - so without going into a “health” discussion, slowly warming the honey to that temperature will make it liquid without affecting the enzymes etc. significantly. Warming the honey beyond 40C starts to destroy them.