Would a person standing on the top tube damage a carbon fibre road bike?
At the risk of getting beat up on carbon will give it a try. 
CF seems to be a sensitive subject.    

I don't agree with your assertion CF are engineered to be strong in certain directions and relatively weak in others.  They are designed to have different flex in certain directions - not weak. 

If I had 4 bikes I need to use as step stools I would go with this order (and I really have all but aluminum):
1) steel
2) titanium
3) carbon fiber (CF)
4) aluminum   

There is a bit of discussion and comments that bearing weight on the top tube is not a stress a bicycle is designed for (and weak).  That is a stress a bike must handle.  If I take a tube and hold it at both ends and try and bend it that is the same type of stress as if I took the tube and put either ends on rocks and pushed on the middle.  The primary force a top tube takes is bending from the ends.  If you watch the video you can see top tube bend and when it fails the two pieces are bending displacement.
Santa Cruz Bicycles - Test Lab
And you can see the CF held up pretty nicely. 

CF takes criticism as it fails brittlely which is true but it takes a lot to get it to fail.  

I would not want to ride any bike that would fail with my weight on the top tube as that is a scenario (crash or drop off) I expect and need it to not fail.  

With that said there is not one CF.  A lot of variance in the construction / layout. 
If you are going to ride a CF then buy a good one. 

I don't mean to advertise a brand but Niner has 5 year warranty including racing. 
I have crashed my Niner Air 9 Carbon hard and not even thought twice about the bike.
I use it for CX training at a local park and stand on the top tube to stash my jacket in a tree. 

There is stuff CF is not good at. 
Don't put a rack on a CF.
Don't take a hammer or bat or hard object to CF. 
Don't take a drill to CF. 
Don't over or under torque bolts. 

I am just amazed at the slow acceptance of CF frames. 
When CF forks first came out there was a lot a questioning. 
But now CF is the dominant rigid fork. 
A fork takes a lot of stress from a lot of directions. 
People think CF is too light to be strong.

I get engineers are misunderstood (and certainly under appreciated) but a simple one foot drop landing on the front wheel is going to put more stress on a top tube than your weight. The frame did not even flex in the picture.  I would not ride a frame I could not jump on.