Members of top-level classes in Flutter's documentation don't get indexed correctly

[Hixie]

We received the following issue (flutter/flutter#47553):

Flutter's Dash docset does not properly index members of top-level elements (classes, enums).

To demonstrate, we can look at how Dash indexes dart:core through its native Dartdoc support.

I bring up Dash, type RegExp., and see that the class and its members are enumerated:

Now, the same with the Flutter docset (which also indexes RegExp):

No members found.

But the type is indexed, here's what we see when we remove the trailing .:

Class and constructor descriptions.

We aren't seeing the members because Flutter's SQLite index is malformed. Instead of including a fully-qualified name of each member, it includes a simple identifier.

Compare:

with Dash's native dartdoc support:

We're not sure whether we're holding dashing incorrectly or if it's something dashing doesn't support. Any ideas?