"This same statement executed outside of the view uses an Index Seek on both tables."

Like you, I get the same plan as the view with a select from a derived table. However, seeks do occur against both tables if separate WHERE clauses are specified with each SELECT of the UNION ALL. So I am guessing that it wasn't really the same statement that Thom ran from SSMS:

SELECT accountnumber FROM agents2009

WHERE accountnumber = 'QOT039365'

UNION ALL

SELECT accountnumber FROM agents

WHERE accountnumber = 'QOT039365';