It's the opposite. A single compromised location can tip a in a national popular election. It almost becomes an arms race of cheating.
With district based they can only affect their district.
Someone wanting to swing a national popular vote fraudulently would need to compromise tens of thousands of ballot boxes to steal on the order of ten million votes -- a much harder ask than compromising a hundred ballot boxes to swing three states in the Senate/Electoral College or gerrymandering twenty districts in Congress.
Easy to detect for a small town, not for a big city, where there are literally millions but who knows how many actually vote. In fact I could cite the exact kinds of statistical reasoning for certain counties in the recent election, but you wouldn't accept that.