Exactly. Whenever TF2 gets serious, it's a surprise, but doesn't feel out of place. The story is exceptionally well-handled. I remember freaking out when Sniper got shot. I couldn't believe it was happening. I actually felt bad for Saxton Hale when he got fired, something I never thought I'd do. The OverWatch lore isn't sure what it wants to be yet, and so it's starting off generic. I hope it grows from there, because otherwise it's just trying to be epic but not really having any effect, conveying more poor writing than actual story.
Actually, now that I think about it, TF2 balances silly and serious in a similar manner to RvB, with everything being silly, and you as a viewer getting used to accepting things as silly, and then getting meaningful explanations for the silly things, even though you had already accepted them. Very intelligent.