I note that the comment section has a very nice answer from Anne.
I dunno what knowledge of horticulture Paul had. But the practice of splicing and grafting shoots from one olive to another is as Anne pointed out are a practice since ancient times. See here for some modern research into old olive trees.
As was pointed out, this practice was done to revitalize a tree so you wouldn't lose it. So it would continue to grow and produce olives for you for many more years.
Sure it is contrary to nature to perform grafting, but we are the stewards of creation and if it helps us and the plant survive it is not wrong. (This would extend to modern technology like splicing plant genetics just as much as husbandry or the evolution of corn over hundreds of years)
As the verse points outs, there are 3 things being referred to here.
- The tree // Olive root (The church)
- The wild branches (The gentiles)
- The cultivated/natural branches. (The Jews)
And if you read further into it is really straightforward.
I am talking to you Gentiles. Inasmuch as I am the apostle to the Gentiles, I take pride in my ministry in the hope that I may somehow arouse my own people to envy and save some of them. (Romans 11:13-14)
If some of the branches have been broken off, and you, though a wild olive shoot, have been grafted in among the others and now share in the nourishing sap from the olive root, do not consider yourself to be superior to those other branches. If you do, consider this: You do not support the root, but the root supports you. You will say then, “Branches were broken off so that I could be grafted in.” Granted. But they were broken off because of unbelief, and you stand by faith. Do not be arrogant, but tremble. For if God did not spare the natural branches, he will not spare you either. (Romans 11:17-21)
Was the method of grafting adopted in Biblical times different? Yes.
St Paul was not aware of the right method of grafting ? No, he seems to be aware of the method that was used. Not like roses, but a living branch, onto a broken branch.
He wanted to bring home to the Romans a great spiritual truth at the cost of factual accuracy in day-to-day horticultural knowledge ? No, but of course he did want to bring them great spiritual truths. :)