Yes, there is a base.  (Side note: this code has changed a lot since I looked at it years ago.  I picked up some of this for my recent cherry-pick answer, which you have linked here.)
Both git cherry-pick and git revert are implemented by the same source files (builtin/revert.c and sequencer.c).
As you say, the tricky part is deciding what to fake up for the merge base.  In your example, we're undoing the B-to-C diffs.  Here's the actual source code (in sequencer.c), stripped down somewhat:
if (opts->action == REPLAY_REVERT) {
        base = commit;
        base_label = msg.label;
        next = parent;
        next_label = msg.parent_label;
        strbuf_addstr(&msgbuf, "Revert \"");
        strbuf_addstr(&msgbuf, msg.subject);
        strbuf_addstr(&msgbuf, "\"\n\nThis reverts commit ");
        strbuf_addstr(&msgbuf, oid_to_hex(&commit->object.oid));
        if (commit->parents && commit->parents->next) {
                strbuf_addstr(&msgbuf, ", reversing\nchanges made to ");
                strbuf_addstr(&msgbuf, oid_to_hex(&parent->object.oid));
        }
        strbuf_addstr(&msgbuf, ".\n");
} else {
[this is the cherry-pick case, included just for completeness]
        const char *p;
        base = parent;
        base_label = msg.parent_label;
        next = commit;
        next_label = msg.label;
When we enter here, commit points to data for C and parent points to data for B.  The assignment to variable base is what sets the merge base, and next-vs-base is what to bring in.  For cherry-pick, the commit's parent (possibly chosen via -m) is the merge base.  For revert, the commit itself is the merge base and the parent (again possibly from -m) is what-to-bring-in.
The other way to get the same effect (which is how this was done many years ago, and until recently, I thought this was still being used) is to reverse-apply a commit as produced by git format-patch.  In this case, the constructed base version is the second hash (the B part from the A..B part of a textual diff):
/*
 * This represents a "patch" to a file, both metainfo changes
 * such as creation/deletion, filemode and content changes represented
 * as a series of fragments.
 */
struct patch {
[snip]
    char old_sha1_prefix[41];
    char new_sha1_prefix[41];
static void reverse_patches(struct patch *p)
{
[snip]
            swap(p->old_sha1_prefix, p->new_sha1_prefix);
The reverse_patches function is called after extracting the text into a series of patches, i.e., after the code that extracts the hashes from the index lines, putting the A and B parts into the old and new prefix fields.  Then (after reverse_patches), when actually applying each patch, git uses the saved old and new sha1 values to fake a 3-way merge (if git am is given --3way).  So by reverse-applying a text patch, we would get the new file as the base and the original as the target, just as with the sequencer.c code.