Sure. And they could also spoil all the votes with an armed robbery - at many polling stations, there's no actual police presence until/unless someone calls them in.

The main intent of all the security measures is that any such tampering be obvious, and that it be clear whose votes (or at least, which precincts' votes) were compromised.

Sure, but that doesn't address an attack that certain precincts that vote a specific party line could be compromised. If 100 attackers at 100 precincts slit some seals than that could swing a swing state

When you have a consistent pattern of ballot spoilage, elections are not counted as normal; at that point you'd have court cases, recounts, assorted forensic attempts to verify valid votes, etc. The system is not a rigid machine - it is a set of rules for the common case, and a set of safeguards that trigger special-case handling.

Basically, a team of 20 voters with boxcutters could spoil the results from an entire precinct.

You would have to assume so...