In fact, connecting a European power tool to US 240V would be hardly different from connecting it to a 133/230V system still used in some countries (supposedly Belgium, certainly parts of Germany in the Berlin area) where single phase appliances are connected across 2 phases of a 3 phase wye system (supposedly Germany even had corner grounded 220V delta systems in some areas). So indeed, the voltage wouldn't matter at all, these tools have to be useable on 230V phase to ground as well as 230V phase to phase.
In fact even electric ranges come with a variety of possible jumper settings allowing them to be used on 230V single phase, 3 phases of a 133/230V system (always tempted to write 127/220V as per the pre-harmonization standard) and 230/400V 3 phases + Neutral (all elements connected phase to neutral), sometimes even 230V single phase 2 hots 2 neutrals (effectively feeding the range with two individual single phase circuits).
