Validity of leaderboard segments

They have segments only on their Garmin connect accounts. They only see them after their ride is uploaded and they sign in to connect on their PC or smartphone. We have that info on our edges.

I guess I will have to hang up my bike.

Or, maybe the data generated from 510's and 810's is not calculated correctly?

I know strava checks for bogus times ( people drive the segment in cars for example). Not sure what Garmin does.

The data is likely calculated correctly, you just have someone with their GPS running while driving. As pointed out above, Strava will automatically flag impossible activities for review, and users can flag them as well. Garmin's segment system isn't far enough along to offer that functionality. I'm sure it is coming, but nobody really knows when.

I have someone on one of my segments that did my hill climb at 29 mph, obviously a fake. Can you delete segments that have been misused if you created them? Or can I, as the segment owner delete these bogus times?

You can delete the segment. If you recreate the segment, the cheater times will end up right at the top of the list again. You cannot delete or flag the bogus times.

Why doesn't garmin recognize that segments are completely useless if people complete their running segments by bike, and their bicycle segments by car?

Agreed, its very annoying that some people seem intent on sabotaging segments. I have a favourite segment, and each time I enter it my garmin tells me & off it goes, my best time is 22 mins so far, problem is the fastest time has been logged as 8 mins, which works out at 38 mph, impossible as there are a few hills in it. So all the time I am racing against a ghost time that is impossible to get near, very frustrating, and clearly the leading time is bogus

My experience of Strava is all and any flagging is user led.
I would say more than 50% of KOMs/CRs that I "lose" turn out to be false.

By far the most common problem is cyclists who record their ride as a run and either don't know how to change it or forget.
The next most likely is people who forget to stop the timer after a run or bike and then upload that plus their drive home.
The other likely reason, especially on short segments, is GPS error.

I can't recall a situation where somebody deliberately "cheated". I am sure it must happen but fortunately I don't think it is common.

Why do you find it so hard to just ride the segment, do your best, and ignore the impossible times? This is all for your personal enjoyment anyway, not determining whether you'll get into the cycling hall of fame or shame. One of my friends took off a few weeks ago, and I couldn't figure out why (but I chased her down anyway). It turns out her son and his friend were the top two on the segment, at around 36 mph! I'm never going to be close to that -- 30 for me would be a miracle. Two weeks later, she was on the tandem with her husband. I told him to "GO!" when they got there. I couldn't hold their wheel. The husband ended up third on the segment. The wife's Garmin lagged his by several seconds and a mile per hour, even though it was mounted on her bars, not even three feet away from his.

So, not only is the segment stuff just for fun, it is subject to the vagaries of the technology.