You should read about the mechanism for acid catalyzed hydration, and then compare it to oxymercuration demercuration.
Hg2+ cation (or maybe HgOAc+ and similar species) acts as a lewis acid in a similar way that H+ acts like a Bronsted acid. It adds to alkenes, and leads to the formation of a cationic intermediate that can then be attacked by a nucleophile. It's a little different because mercurinium ions don't undergo carbocation rearrangements. A better expression than "fancy proton" would be "soft proton." This is because the mercury cation has a preference for bonding to different things than a proton due to hard/soft acid base chemistry. Mercury prefers alkenes and certain weak bases with large and fluffy (polarizable) atoms like sulfur, whereas a proton will have a higher affinity for traditional bronsted bases like amines.