I'm thinking the person who told me that PI was on the drengin tree may have been confused with something he picked up in trade.
It's very possible that the other person did get it from a trade. When you trade for a tech, it will replace the equivalent tech in your own tech tree with the version from the civ with whom you traded.
If you do not have an equivalent tech, the tech is merged into your own tree based on its tech requirements. So if you have this tech tree:
A __> B
and you trade for tech C (which is not naturally in your own tech tree), and C requires A, it will be merged in like so:
A ___> B
\___> C
The same thing happens for stolen techs as well.
So if the other person got Planetary Improvements, it would show up in his own tech tree screen when he viewed it.
Techs shouldn't be invisible and then pop up when you research their requirements. This should only happen for ethics-based techs. There is a button at the bottom of the research screen that will allow you to hide future techs. You could check to make sure that is off. Just click the one in the middle and it should show everything.