Well there must be a leak somewhere behind the baseboard and what you see is mold so you need to take care of this quickly.

I agree, it is moisture from a leak. The only permanent fix is to have someone take it apart and see what is leaking and then have the repairs. Yes, the black appears to be mold.

I had cut out that part of the baseboard during repair but there was no leak. Does it make sense to put a PVC/vinyl baseboard there instead of MDF?

You have a leak.

Remove baseboard again, and leave it all off for several days, you will eventually see water.

You need to rip out more than that baseboard. You have a leak not a baseboard problem.