I don´t think we can judge this so easily, but i could give my bit of experience with theory here.
The assumption with "negatively charged" particles... I thing i get somehow what it should mean:
metal ion in solution is positively charged (cation). in order to get it back to the metal, it must come to the contact with some "negatively charged" particle, which give the electrons to it, make it precipitate as non-charged metal.
I will not consider it this way, but in very simple (and clearly somewhat misleading) way, OK. Could be used to disclose chemistry in "friendly way" for non-chemists
Thing is, as it was stated by more of us here, compound which cause metal cation to go back to the non-charged metallic form need not to be charged. It just need to have some electrons to offer
Here we come to thing called "redox potential". I think the best approach to disclose what is happening in your pot.
All particles/chemicals in your solution want to get in the form, where they would have the lowest energy possible. There are chemicals that very kindly pass electrons, and there are chemicals that very kindly accept some. Ones are in our eyes "reducing agents" and the others "oxidating agents". Oxidants accept electrons, reducers pass electrons.
This is when the "redox potential" comes into the game.
Redox describes certain half-reactions in volts, compared to so called "standard hydrogen electrode". Not exactly needed to explain what it precisely is, but it is our "zero potential".
As we mix together two chemicals, say gold chloride and sodium sulfite, they will interact together.
We could describe this in two half-reactions:
-reduction of Au3+ to metallic gold: Au3+ + 3 electrons ---> Au(0)
-oxidation of sulfite to sulfate anion: SO3- + H2O - 2 electrons --->HSO4- + H+
We focus only on the electron transfer reactions. Everything else is ommited for clarity. Sodium and chloride ions combine to make NaCl, but really they dont gain or loose electrons, so they dont figure in half reactions.
Both have they redox potential. Half-reaction with gold has value of +1,40 V. Half reaction for sulfur dioxide has value of +0,40 V (these values differ as temperature, concentration and other ions are taken in consideration).
When combined to give result: oxidant minus reductant. +1,40 - 0,40 = +1,0 V
Value is positive. This indicates, that reaction will proceed.
If we take copper for example:
Cu2+ + 2 electrons ---> Cu(0), this half-reaction has potential of +0,34 V.
If we try to combine this copper half reaction with above sulfite reaction, we will find that +0,34 - 0,4 = -0,06 V
Value is negative, so reaction will not proceed.
This is theory. In real world, ions are complexed with other ligands (AuCl3 in solution likely form AuCl4- = lowering the energy), temperature, concentration and other factors hassle with these ideal conditions numbers.
But this is what is happening. It could be considered as some kind of trade.
When somebody try to sell you some stuff, you could accept or reject the offer. The same happens with chemicals in your pot. Copper in solution rejects the sulfite offer, but gold kindly accept it