Based on personal experience (echoed by forum threads such as this one), I hold it for true that intonation may suffer from extreme string angles (either too flat or too sharp) above the nut or below the bridge saddles.
This issue proved somewhat controversial in another thread which I wouldn't like hijacked to respect the OP. Plus creating a propper thread devoted to this question might bring it to the attention of even more people knowledgeable on that particular subject.
Thanks for reading this post and looking forward to your input.
Have a great day,