Their statement is just wrong.
Because government spending is included in GDP, GDP does not properly reflect “the economy.” Because it doesn’t properly reflect the economy, the question of whether it grows from year to year or from quarter to quarter is irrelevant.
If I were to propose to you that we can measure the strength of the economy by how many baseball games the Chicago Cubs win in a year, you would say that’s crazy. If I tried to say “Well it doesn’t matter if that’s crazy because at the very least we can look at how many games they won last year and compare it to this year and see if things are getting better or worse” that would be a ridiculous statement. Garbage in, garbage out, you know?