Can you run following under msdb and see if you find DENY on sp_send_dbmail and

GranteeName is not the user or any associates role?

If you have GRANT and DENY, DENY will take precedence

SELECT

dp.class_desc, dp.permission_name, dp.state_desc,

ObjectName = OBJECT_NAME(major_id), GranteeName = grantee.name, GrantorName = grantor.name

FROM sys.database_permissions dp

JOIN sys.database_principals grantee on dp.grantee_principal_id = grantee.principal_id

JOIN sys.database_principals grantor on dp.grantor_principal_id = grantor.principal_id