Why does mutarotation occur only in specific media?
Essentially, it is just the formation of the open chain form, and then back to the other cyclic anomer, right?


Precisely, mutarotation involves interconversion of the α-and β-forms (cyclic anomers) of the monosaccharide with intermediate formation of the linear aldehyde (or ketone).



The mutarotation of glucose is a general acid- base-catalysed reaction which involves two proton transfers. Studies have proposed that these proton transfers are either carried out in a stepwise or concerted manner, with the latter alternative possibly incorporating several water molecules in a cyclic transition state.



Two possible mechanisms of mutatoration have been investigated:


The first involves an intramolecular proton transfer i.e acid-catalyzed reaction.
The second uses one solvent water molecule to assist proton transfer i.e water-catalyzed process.


There is some experimental  evidence1 for the solvent participation in the mutarotation reaction that appears from the studies of primary solvent effects on the rates of glucose and tetramethylglucose observed in $\ce{H2O + D2O}$ mixtures. In addition the absence of intramolecular proton transfer can be deduced from the small values found for the mutarotation rate of glucose in organic solvents.


  Eigen1 proposed that the two proton transfers could proceed
  in aqueous solution via a pathway involving two or more water
  molecules in a cyclic hydrogen-bonded transition state, where the
  intramolecular proton transfer does not take place in aqueous
  solution.


Previous studies2 have shown that the reaction order with respect to water is zero for an acid-catalyzed reaction involving a stepwise mechanism, however in aqueous solution without added catalyst, water molecules must act as an acid or base and it is possible that the mutarotation reaction does proceed via a cyclic-concerted mechanism involving about three water molecules.


  The results obtained in experimental work in the  newer
  studies1 have shown that mutarotation is a
  solvent-assisted process that obeys pseudo first-order kinetics. Besides that, the first water molecule from the solvent acts as a
  catalyst, and plays a decisive role, since it completely changes the
  mutarotation mechanism.


So a solvent is necessary, the evidence been seen  in proton transfers in  reactions that do occur via cyclic concerted mechanism as proposed in these studies.



References:


A theoretical study of glucose mutarotation in aqueous solution. A. M. Silva et al. / Carbohydrate Research 341 (2006) 1029-1040. Carbohydrate Research 341 (2006) 1029-1040.
The Mutarotation of Glucose in Dimethylsulfoxide and Water Mixtures. Ballash and Robertson CAN. J. CHEM VOL. 51. 1973.
CM Garrett, Grisham Biochemistry