I believe that you are partially correct.
1. Sample size: you tested this with a sample size of 5. With a failure rate of 70% there would be a 24% chance of this happening. This probability is it rather high. Thus what happened on this video could easily be a fluke. If you were then to do a 5 sample test with 1 million luck and fail 2 of them nd you concluded 1k is better than 1 million LK and you were to publish it in a scientific journal, you would be rejected. You would have to conclude your study in a way similar to this:
"Results indicate that 1k LK has a higher success rate than 1mil LK. However due to the low sample size, further testing is required in order to comfirm this."
I would say, in order to make your claim, you will need to test out on at least 100 samples in order to gain a result that could tell you something. (It may be within 5% error)
2. The nature of how it works: I assume that LK will affect fullhouse within a particular range of LK. If LK is below the range, success rate will take the value of some preassigned minimum, within the range success will increase with LK and above the range, success rate will cap such that any extra LK will not be of any help (except for the addition of damage).
1k LK is below the range so it will take on the min success rate. I do think the kTO and jTO players will have done extensive tests in order to claim that LK helps.
I also do not think that the min and cap are much different (say 20%). When grinding, this is significant enough to be noticed. (80% will have twice the number of fails compared with 90%)
In terms of FH damage, the damage increase from 4114 to the damage increase of 1144 is 2:1. In terms of total benefits for each of the stats the ratio is.
Ap:Lk:Hv
16:8:12
Assuming 16AP is equivalent to 1 LK
