@Orgopete - Sorry, I could not understand what you meant.
My question is, precisely , is - is it plausible to think/how is it justified that the protonation of a carbonyl oxygen can lead to sufficient positive charge on the carbonyl carbon for a carbocation 1,2 shift to take place, as depicted on MSU website? In my opinion it is not plausible because there would not be sufficient energy for the rearrangement to take place. Recall why rearrangements do not occur in SN2 reactions. Why? Because there is delta plus- not sufficient energy.
Can you post some other literature/ reference which depicts the mechanism shown on MSU website ( for example 1 ) , hopefully with more clarity and reasoning?
Re: rearrangement reaction in SN2 reactions
Remember, SN2 reactions are on the nucleophile initiated end of the substitution spectrum. In SN1 reactions, bond breaking occurs before bond formation. In SN2 reactions, it is the opposite, bond formation precedes bond cleavage. The bond formation increases electron density on the target carbon, it would be unusual for a rearrangement to occur. If a reaction were to be more SN1-like, then you may see this happen. Reactions can be thought to occur somewhere between the two extremes I have noted.
Re: ability of a carbonyl carbon to attract electrons, rearrangement or addition
My argument was simple, although it is unusual for this reaction to take place, it should be taken in context of all carbocations. Granted that non-bonded electrons of an attached oxygen will limit the attractiveness to that carbon, but this should also be taken in context of are there any attacks? Yes, ketalization and hydrolysis involve direct attack upon a carbonyl carbon. Even an enolization must be an attraction of the C-H electrons to the carbon.
Perhaps it is unusual for a carbon to migrate, so the instances are limited to groups that can provide greater stabilization that normal, such as the diphenyl case. I also noted that Reusch suggested that a protonated epoxide may be considered. I'd also concede that though Reusch did not give any compelling examples to argue this point.
This is my perspective upon this question and chemistry in general. Our models are not complete. It isn't possible to have partial charges, for example. Electrons are negative and protons positive and only involve full charges. If you compare the oxygen of hydroxide, water, and hydronium ion, the oxygen is +8 in all instances. What changes is the number of protons attached to the electrons. They have an effect upon the electrons and their availability, but no effect upon their charge. If you use this perspective, then you may look at reactions a little differently. It isn't whether a functional group should react in a certain way, it is how the assemblage of atoms may affect the electrons. For example, you may find some books write a hydroboration reaction as though it were a (symmetry forbidden) 2+2 reaction and HCl does not. Borane is a Lewis acid and is attracted to the electrons of an alkene. What I ponder is how this should affect a reaction, for example, boron holds its electrons much more weakly and its bond lengths are greater.
I have included a scheme and I suggest it should not be unusual to see attack upon a protonated carbonyl at the carbon atom. Enolization can be thought as a neighboring group reaction. The rearrangement may not be a general reaction (hence my error in assumption about it). I think the examples given are consistent with other chemistry. For example, protonation of an enol ether can be written with the same intermediate as the enolization step. If that is correct, then migration of a phenyl group may also occur similarly, especially if it were to lead to a "stabilized carbocation". (I too found it difficult to think of an carbocation alpha to a carbonyl group to be more stable.)
Granted, mechanisms are rationalizations. I agreed with Reusch's mechanism. It seemed plausible and consistent.