If you do not need the rank in your output (and it appears from your comments and favored answers that you do not), you can simply combine the quiz scores nearest to Jan's score:
Query (SQL Fiddle here):
-- XXX this assumes `scores`.`username` is UNIQUE !
SELECT * FROM (
-- Get those who scored worse (or tied)
( SELECT s.*
FROM scores s
CROSS JOIN (SELECT score FROM scores WHERE username = 'Jan') ref
WHERE s.score <= ref.score AND username <> 'Jan'
ORDER BY s.score DESC
LIMIT 2)
UNION
-- Get our reference point record
(SELECT s.* FROM scores s WHERE username = 'Jan')
UNION
-- Get those who scored better
( SELECT s.*
FROM scores s
CROSS JOIN (SELECT score FROM scores WHERE username = 'Jan') ref
WHERE s.score > ref.score AND username <> 'Jan'
ORDER BY s.score ASC
LIMIT 2)
) slice
ORDER BY score ASC;
(Note that I LIMITed the results to two records before Jan and two after Jan because your sample data set was so small.)
Those parentheses on the constituent queries above are needed to allow LIMIT and UNION to work together. The outermost query then lets us ORDER the results of a UNION.