My boss says that text should always be edited in the native file. It's much easier for me to edit the text in a PDF in Acrobat Pro, though. Is he right? Are there instances where the text will not render if edited in Acrobat Pro?
Yes, 100% right. If you have the native file you should make changes there and then create a new PDF file from it.
PDF files were never meant for such editing tasks and doing so can go wrong very quickly, so you should avoid it, if possible.
100% agree with your boss and “try67” ...
The text editing feature of Acrobat was designed more as an emergency “text touch up” feature than a text editor.