No, angle of penetration matters in both games.
The only online article we could find covering this suggests that the angle matters in Portal 2, but did not in Portal 1, but after doing science, we can clearly demonstrate that the article's wrong - entry angle matters in both games.
Since you asked for undeniable proof, the following videos show you this mechanic in Portal 1.
4 tests on the lastest version of Portal 1
Tested on June the 6th, 2014 :
- Portal placed vertically : If speed vector was normal to the wall, I should
not pass through the emancipation grill
- Portal placed horizontally : I use the Angle of entry in the orange portal to land way further than the blue one.
- Using a ball instead of Chell :
(If you are only going to watch one video, make it this one) I tested this on advanced chamber 17. The ball falls through the blue portal and gain momentum (while falling). During the fall I place an orange portal above the slanted surface, as soon as the ball comes out of the orange portal I place another orange portal on the slanted surface giving the ball an angle of penetration (45° I assume), the ball is then ejected out of the blue portal but not vertically, it's propulsed against the wall just in front of me. I repeated this operation several times with different portal placement in order to be sure that this was not due to a collision of some sort and it's not, the outcome should be quite easy to reproduce if you want to test it by yourself.
To clear the doubt about the ability to move in the air (allowed by the physics of the game) :
Here's a last video : I start moving away from the portal as soon as I enter the blue portal with speed and try to go the furthest as possible. With a better momentum (than in the Horizontal demonstration) I can't reach the same distance (by far) as in the said demonstration. This tend to prove that even though moving in the air allow some liberty, angles do indeed matter.
To finish : in Portal 2 angle matters aswell but it's way easier to show it since its part of the gameplay with lasers.
Some other examples in Portal 1 and explication
Example on vertical surface for Portal 1 : In this example you can clearly see that the angle of penetration is conserved at the exit, allowing to reach the plateform on the left when exiting the portal. This custom map has for purpose to show those kind of mechanics but it can be reproduced quite easily on any official maps.
Example on horizontal surface for Portal 1 : In this example you enter twice the blue portal and goes out of the orange portal at 2 different angles (and speed but that's not the point here) allowing you to reach the top plateform. If the exit velocity vector was normal to the surface you wouldn't be able to reach the top plateform at all.
This mechanic is for example what allows to finish the room 15 in 1 step in the least step challenge. Once you get into the "loop", you can place a blue portal on the ground and reach the elevator thanks to the momentum and the angle of exit (given by the angle of penetration). Again here, if the exit velocity vector was normal to the ground, when the blue portal was placed Chell should just have jumped vertically. Obviously it's not the case since she reaches the elevator.