I would say for injecting into ball joints like that you'd need as heavy an oil as possible, maybe even CV joint type grease if warmed could be injected by such a method.
I do similar injecting the correct moly grease into CV joints, i have an adaptor Sealey make which attaches to my grease gun, this looks like a long thin pencil with a rounded but narrow tip, its hollow and by snipping the small end of the joint's boot clip then slide the attachment under the boot tight up into the joints and pump away to my hearts content...but that adaptor would be a bit big for ball joint boots to reseal i would think.
I've been doing this since i had dark hair, which is a long time ago let me tell you, and to date can't recall ever having to replace a CV joint on any car, even if a joint starts rattling often enough regreasing like this will see it last the rest of the life of the vehicle.
I have some thin stainless steel jubilee clips which i use for resealing the end of the boot, cable ties just don't cut it and i'm bloed if i can get on with the supposed DIY systems for replacing such clips, sure my neighbours have learned a whole new vocabulary during my efforts with those kits.
No reason why doing as the video suggests wouldn't see ball joints last forever too, i did wonder at one time if it would be worth drilling into the stamped bottom cup of said ball joints and fitting a grease nipple would be worth doing, enable regular normal greasing but its something i never got round to experimenting with, i did find some blanks fitted like that in one car i owned, looked like a factory job...wonder if that was my 70 series? removed those blanks and fitted grease nipples, i also kept the hub swivels well topped up with CV grease on y 70 and they never gave any bother either.
Good greasing is a must, not LC related but between services i notice the road tanker i drive can feel 'reluctant' to stay in a straight line over typical motorway grooves, the fifth wheel/ rubbing plate on tankers is quite exposed to the elements, more so than other tyoes of semi trailer, a quick regrease of the fifth wheel sees it back to perfect.
At one time British built lorries wre fitted with 'autolube, which was a heavy oil/grease dispenser bottle and puump and a myriad of small bore pipes which went from this bottle all around the chassis to every joint and spring shackle, with oil/grease pumped all around the vehicle at pre set intervals, it worked which is why no one uses such things any more because vehicles lasted too long.