How can INDEX rebuilds be going parallel when MAXDOP is set to 1
It is running a stored procedure named proc_DefragmentIndices in many (possibly all) of these databases at a time.
The stored procedure rebuilds every index in the database unconditionally.

I assume you don't have any control of this, but I'd be remiss if I didn't suggest that you make this stop happening as soon as possible   Use Ola Hallengren's script, which will at list rebuild or reorg only at specific fragmentation thresholds.  Or considering avoiding index rebuilds in favor of statistics updates.

How can INDEX rebuilds be going parallel when MAXDOP is set to 1?

They shouldn't be.  And they really shouldn't be because you're using Standard Edition - and parallel index operations are an Enterprise Edition feature.  I wonder if there is just something weird about the way this is showing up in Activity Monitor.

Activity Monitor shows the ALTER INDEX commands but sp_WhoIsActive does not. Does anyone know why?

That's another red flag that something is off here.  Index rebuilds should show up just fine in sp_WhoIsActive.  Here's me rebuilding the Posts table (from the StackOverflow2010 sample database) on my laptop:
USE StackOverflow2010;

ALTER INDEX PK_Posts__Id ON dbo.Posts REBUILD;


As a further point of investigation, you could query sys.dm_os_tasks directly when you see one of these ALTER INDEX sessions that appears to have gone parallel, to be extra sure whether it's serial as it should be, or parallel.