Hiya, Nick! There are never any silly DNA questions, only silly answers. Wait. That didn't come out quite right...
Anyway, if I have the inheritance chains correct, through your paternal grandfather, Michele, Giuseppantonio and Arcangela are your 4g-grandparents. And through your paternal grandmother, Louisa, Giuseppantonio and Arcangela are a generation closer: your 3g-grandparents.
To Antonia Venditti, your 2g-grandmother, her profile shows "~6.25%" sharing with you, which is correct...works out to the same as would be a 2nd cousin or great-grand aunt/uncle; ~425cM in centiMorgans.
Agostino Venditti, Antonia's brother, is also your 3g-grandfather. His profile is showing "~3.12" with you (or ~212.5cM). Which is also correct...though that calculation isn't taking into account that Agostino is both a 3g-grandparent and a 2g-grand uncle. This may be an example of an issue with the algorithm, I'm not sure (you should also show ~6.25% with Agostino, not ~3.12%), but we aren't concerned with that right now; it doesn't impact the sharing estimates with Giuseppantonio and Arcangela.
So... Giuseppantonio and Arcangela are both your 3g-grandparents and your 4g-grandparents, genetically speaking. That means you'd be expected to share (theoretically/hypothetically/approximately) about 3.125% down one inheritance path, and 1.5625% down the other.
Et viola! Give or take 4.6875% combined. So, yep, the ~4.69% is correct!
As a practical matter, this is also a good example of how the genetic-sharing impact of pedigree collapse lessens quickly over successive generations. I haven't looked further at your part of the tree, but let's say that a third child of Giuseppantonio and Arcangela--let's say Maria Rosa Venditti--has a descendant of a contemporary generation to yours who takes one of our popular microarray DNA tests. Let's also assume that her line has no pedigree collapse between your mutual 4g-grandparents, Giuseppantonio and Arcangela.
On paper, you would be 5th cousins, sharing a pair of 4g-grandparents. At that relationship level, you would only be expected to share about 0.0488% of your DNA, call it about 3.3cM. But you also have a path to Giuseppantonio and Arcangela as your 3g-grandparents. If we consider that path instead when comparing you to your new-found cousin, the two of you would be 4th cousins 1x removed, and would be expected to share about 0.0977% of your DNA, or about 6.6cM.
At this stage it's simple addition. Your new cousin is both 5C and 4C1R to you. So your expected sharing would be 0.1465%, which would work out to 9.962cM. As you can see, we're talking very small differences over the course of those six generations thanks to the dances of meiosis and independent assortment going on in the chromosomes at each birth event. The difference is so small, in fact, that the extrapolated calculations from our microarray tests can't even really measure it with great accuracy. The numbers would be more interesting between you and, say, a descendant of Maria Michela Venditti, but it is an example of how single instances of pedigree collapse don't affect current-generation sharing as much as some might expect. Which is a good thing. Otherwise, in regions where populations are small and isolated, there wouldn't be sufficient genetic diversity to support the species.
See? Going from your simple question about 4.69% DNA sharing to a statement about genetic survival of the human species... I told you DNA answers could get silly.
Edited: Had to take a second look at Venditti-14. I think--but don't know--that this, and Venditti-13, may be examples of the algorithm not taking into account all inheritance chains for the percentage calculations.