I doubt very much the government could run two information campaigns at once.
Not because they're incompetent (they are)- either by design or just naturally - but rather, the general population.
We've had, for however long it's been now, the slogan "Stay Home" thrown at us incessantly, and still people of all intellects from World-renown writers (Neil Gaiman),down to the village idiots, and as far down as Prime Ministerial advisers have ignored it- it couldn't have been simpler, even my dog understands it.
So, going by the lowest common denominator, they'd be throwing too much information out there.
Executive Summary- people too thick for two bits of information.