Question regarding the mechanism of oxymercuration-demercuration of alkenes
This reaction, in my opinion is an extension of Markovnikov’s rule 

To understand why Markovnikov’s rule works, consider the
structure and stability of carbocations and about the general nature of reactions
and transition states.

The first point to explore involves structure:


  A great deal of experimental evidence has shown that carbocations are
  planar. The trivalent carbon is sp2-hybridized, and the three
  substituents are oriented toward the corners of an equilateral
  triangle.


Because there are only six valence electrons on carbon and all six are used in the three s bonds, the p orbital extending above and below the plane is
unoccupied.

The second point to explore involves carbocation stability. Thermodynamic measurements show that,
indeed, the stability of carbocations increases with increasing substitution so that
the stability order is tertiary > secondary > primary >methyl.



Now here comes the question…

Why are more highly substituted carbocations more stable than less highly substituted
ones? 

There are at least two reasons. 

Part of the answer has to do with inductive effects (as you noted in question) , and part has to do with hyperconjugation. 


  Inductive effects, result from the shifting of electrons in a s bond
  in response to the electronegativity of nearby atoms. (electrons from
  a relatively larger and more polarizable alkyl group can shift toward
  a neighboring positive charge more easily than the electron from a
  hydrogen


. Thus, the more alkyl groups there are attached to the positively charged carbon, the more electron density shifts toward the charge and the more inductive stabilization of the cation occurs)

Hyperconjugation, is the stabilizing interaction between a p orbital and properly oriented C- H sigma bonds on neighboring carbons that are roughly parallel to the p orbital. The more alkyl groups there are on the carbocation, the more possibilities there are for hyperconjugation and the more stable the carbocation