The two other answers so far suggest you will probably be OK.
That would not be my expectation.
Many people report not having had problems, but here are a few reports of confiscated tripods:
Here someone comments on twitter
Having your tripod confiscated at security despite being allowed it on 7 other flights this summer is not the one #cheersfrance
and here is an "wasn't confiscated after he argued long enough" story.
One reported tripod confiscation here but many others report no problem.
Report of confiscation of a tripod by UK customs here
ie it seems that while you will often be OK there is no guarantee that a tripod will not be confiscated occasionally.
I've found Australian security people to be amongst the toughest on occasion. On several occasions I've seen them set up their own XRay and screening system 'at the gate'. I've seen these people confiscate unopened drink bottles which were bought from vending machines in the gate lounge (ie after main security has been passed.
I've had an inkjet refilling cartridge confiscated by Chinese internal security at Guilin airport when travelling to Guangjho. The refiller was unopened. It had 3 tiny internal needles - maybe 10 to 20mm long and shrouded inside the filler. As a weapon it would rank well below an airline meal tray.
I've heard multiple stories of nail clippers being confiscated. These may be useful for inflicting pain if you pushed them up somebody's nostril - but kicking them in the shin would hurt them far more.
The inkjet refiller had already passed successfully along the route NZ-Brunei_HK-China. Internal Guangjho-Guilin.
ie the security people do not have be reasonable or logical or rational or fair. They can assess what they wish as a threat and may do so. A tripod has long pointy parts and could also be used as a swung weapon (The fact that jumping on a tray table and breaking it off would produce a far more dangerous weapon is irrelevant).
It sounds like Doc has been exceptionally lucky and/or is exceptionally charming.
Your tripod may survive the trip.
But, if it didn't I would not be in any way surprised.
I'd not take a tripod that I was not prepared to lose as carry on luggage.
Something like a gorillapod or a bean bag tripod would be far more likely to survive and may be almost as useful.
A customs/security man having a REALLY bad day just might mistake a Gorillapod for an inkjet refiller and confiscate it. But vanishingly few would mistake a beanbag for a fingernail clipper.
Examples of Gorillapods or clones and examples of use in demanding situations.
Example bean-bag "tri"pods.
Also handy if you meet a Leopard (or whatever).
Using beanbag tripods:
DIY bean-bag tripods.
Commercial bean-bag tripods:
Note: Gorillapods are unlikely to make good pillows.