What he is saying is that Vaynes Silver Bolts only work every third hit on the same dude. So she basically gets a max of 2% true damage and 20 free AD on average (best case scenario).
This is good and all, but it is not enough to rely solely on Bolts to deliver your DPS. Compare to Kog who has a 6% damage proc on EVERY SINGLE ATTACK (even though it is magical, not true). Kog simply gets more Deeps out of his steriod and thus can use on-hit/AS booster items like Wits End. Kog gets ZERO AD boost, and nothing really scales off of AD either (excluding his ult which scales crappily)
Other reasons to avoid the on-hit items are:
a) The AD on 3rd hit is actual AD, not a 60 dmg proc. Hence it can CRIT.
b) Her Tumble boosts her damage based on AD, not on-hit damage procs. A wits end does nothing to work with tumble.
c) Actually Tumble kind of boosts her attack speed (or can actually slow it down at a point), making AS less important than you might think. Corki players will kinda know what Im talking about here.
Hence, you want consider Bolts true damage as a nice bonus, NOT as something to base the entire champ build around. She still gets free AD and AD-scaling from tumble, so you still want to be able to hit pretty hard per attack by getting both AD and CRIT. This does not mean ignore AS though...just to not overly focus on it.
Another reason to avoid WitsEnd/Razor/etc, is because Phantom is already really really good for Vayne. The crit works very well with her AD-centric ness and the movespeed bonus is very very good. WE/SotD/Razor do NOT boost her MS, and if you DO combine them with PD, then their onhit dmg doesnt crit and thus doesn't combo well.
I am not saying it fails utterly, but that it is just not as efficient as it could be with the correct itemization.