That woudl explain a higher death rate in those countries, but not a higher transmission rate.
To me, when you see how the curve was flattened so effectively in South Korea in particular, it's quite clear that the cultural difference in Spain/Italy played a huge factor in the transmission rate skyrocketing.
For the UK/US, it's a bit different. It's skyrocketing here mostly because we're just an incredibly stupid populace who don't use common sense, simultaneously led by braindead donkeys.
Well that's probably true but at the moment people are following the rules and measures so we just have to hope this time next week (so 2.5 weeks into lockdown) we've at least started to see the flattening of the confirmed case rate.
Key to it all also is testing and more testing and more testing and having pumped money into the NHS in the proceeding months (and I know, we didn't do any of that).