Do you guys have any experience having the servers in the US for non-US start-ups?
But did you hear it from a tax attorney / certified accountant?
That being said (and: I've no experience in Sweden, and I'm neither atty nor acct) the idea that a US tax liability could be incurred by an international corp/business purchasing a service (e.g., AWS) from company in U.S. ...seems pretty outrageous.
If you're selling a product/service then where you're servers are located can matter for state sales tax collection. For instance Texas considers databases warehouses for state tax reasons, which creates "tax nexus" a term of art in taxation with Texas. Once tax nesus has been created then you would have to collect texas state sales tax which is 8%+ (check rates) for everything you sell in state, and if you don't collect it from customers when you sell it you still owe it to the state and can't go back to the customers to get it!
All I can say is that it's a lot cheaper to spend money on an hour or two of an experts advice before you do something than to fix a mess later. If you're in startup mode it sucks, but may be required.
What you haven't specified is if you are concerned about the cost of hiring the equipment (a purchase and therefore tax deductible) or the sale of your goods or services.
For the record, your company earnings from sales are taxed according to the country in which the company is declared and owned and where the company accounts are filed. It has nothing to do with the location of the servers on which your software resides.
Double taxation [treaties] are not what you have assumed them to be - they do not necessarily mean that you are taxed twice and more specifically they relate to individuals earnings and not companys'.
As I say you have mixed a lot of issues into one question.
There's no nexus as long as you aren't co-locating servers that you have purchased yourself. If you're leasing from AWS (or most dedicated server providers) there are no issues.
The US doesn't care what Swedish companies do, unless you establish a physical presence in the US (or does something that forms a nexus, and even then, that varies by state).
You don't want to go anywhere near the US tax system, because it's pretty much the worst tax system in the world. Avoid it at all costs.