Actually DCM is by far not as inert as many people would like it to be. Apart from its being suspected to cause cancer (DNA-alkylation) I´ve seen it to react with a variety of nucleophiles.
I know of an attempt to prepare malodinitrile by action of cyanide on DCM. No malodinitrile has formed, but there sure were some new peaks in the reaction mixture.
A mixture of toluene, pyridine and DCM prepared as GC standard (industrial recycling plant for pyridine) produced glistening white needles after a few days standing.
Toluene and pyridine alone don´t do that.
I was wondering myself at how DMT and DCM might react and since an alkylation must be the first step it is probably reaction with the terminal nitrogen to some kind of quarternary compound, which then reacts with the indole at 2-position, losing HCl. If one methyl of DMT gets lost (maybe as CH3Cl?), voilá - there we are: 2-methyl-tetrahydro-betacarboline.
Remember: DCM is also some kind of camouflaged formaldehyde!
Build a methylene bridge between the terminal N and the indole, split off a methyl, there you are.
Nasty stuff! Whenever you get a freebase in DCM, work fast, work at the lowest possible temperatures and be sure to remove all(!) of the DCM (hard vacuum, codestillation) as you work up.
Better still: Avoid DCM!