Pages 174 to 181 of Transhuman cover nanofabs in a lot more detail. But from what we're shown with nanohives on page 328 of 1e Core, nanohives are their own dedicated thing and producing unique nanobots requires a larger more dedicated hive. That said those hives aren't exactly huge, 30 centimeters on a side with 25 liters of volume is the smallest they go unless you're using tiny nanohives that produce one specific type of nanobot. Still it looks like producing nanobots requires a dedicated machine to do and given the level of precision we're talking I can believe that.
Now I do think nanofabbers can make microchips and work on the nanoscale, I just don't think they have the precision to create nanobots or microbots. It's one thing to create indentations or trace lines in the nanometers, it's another to create a machine at that size. If you're looking for a specific rule that spells this out I haven't found it, I'm just working off the fact large nanohives are treated as entirely seperate from small sized fabbers.
(Also page 342 for 2e gives nanohives a lot of much needed detail if you're curious)