This wasn't the UK government, though, but Parliament through its Commons Digital, Culture, Media and Sport Committee.
Parliament doesn't allow government ministers to be members of parliamentary committees, only backbenchers, as Committees are one of the main ways that Parliament holds the government to account.
In American usage, "the government" is the totality of the body which exercises sovereign authority. All MPs, minister or backbencher, are part of the government, because Parliament is a government body. Similarly, any official action by any part of Parliament is an action of the British government.
Bluntly, Parliament is Parliament. (Her Majesty's) Government overlaps it, but is not the same. The DCMS committee in particular scrutinises government, but isn't part of it. I guess you could describe Parliament as being able to exercise (a few) State powers, but they really aren't a branch of government on the US theory.
Das wage ich zu bezweifeln.
A committee is not of government as it will include MPs from all sides, and seeks non-partisan balance no matter which party is currently in government. The Digital, Culture, Media and Sport Committee currently has 5 members from each of the main parties and one from the LibDems.
Committees can, at times, be quite strident in their criticism of government.