Consider the following search results, both of which return 'Si Cranstoun' as the top hit:

http://musicbrainz.org/search?query=si+cranston&type=artist&method=indexed
http://search.musicbrainz.org/ws/2/artist/?query=si+cranston&dismax=true

Having inspected Search.pm, the dismax argument is being added by default for a simple search. However, it is not being added by default for the following web service search:

http://musicbrainz.org/ws/2/artist/?query=si+cranston&method=indexed

The real problem being that adding a dismax argument doesn't seem to have any affect either:

http://musicbrainz.org/ws/2/artist/?query=si+cranston&dismax=true&method=indexed