Almost a nice question, but actually not correct. The assumption that the server default language is us_english isn't adequate; you have to assume that the default language for the login used to connect SSMS to the server is us_english, because the new query will use a new session, which will use the login's default language, not the language that has been set for the first query's session, and the login's default can be different from the server default. The set statement commented "just to make sure" in the first query merely makes sure that the session containing that query will use us_english, not that the other session will.
In SQL 2012 there's another complication - if it's a contained database, the second call will use the databases default language if the login hasn't set a different default language, and the databases default language may be different from the server default. Was that what the instruction to connect to the same database for the second query as for the first was about? If it's not a contained database, the database is irrelevant; and even if it is, the assumption you need is that the login's default language is us-english. so the database would be irrelevant if the right assumption had been stated instead of an inadequate one.