A royalty free image with a one time purchase means that the person purchasing it is granted the rights to reuse and distribute the image as much as THEY want. It is not giving rights to everyone who they distribute it to to then redistribute it.
With royalty free images, you don't have the copyright to the image, you only have a right to redistribute and you can't transfer that right to any other party unless the license agreement specifically allows it to be transferred (and in that case, likely only transferred to one person.)
Thus, having a copy of a royalty free image does not allow you to reproduce it unless you also have the right to redistribute, which is what you purchase.
If you want images that do not require a fee, you can look for open images or public domain images. Open images are images licensed for free use, such as through a Creative Common's license. There are still license requirements on what you can do, such as requiring non-commercial use or requiring attribution, but you can use such images freely as they are being licensed for free use.
Public Domain images are images which have either been released from copyright or on which the copyright has expired. These images can generally be used in any way shape or form as there is no rights holder to the image anymore, though public domain law may vary some in your jurisdiction, so it is good to check if things like attribution are still required.