A company that is based in the US without a US bank account might be a red flag to any payment processor. The easy answer is open a US based account for the business and have the funds transferred, however, there are likely some tax consequences you would have to explore.
Stripe isn't perfect, but my bet is that they don't get to make a lot of these types of decisions. From my understanding when you become a gateway/clearing house there are all kinds of rules Visa/Mastercard etc place on you. It is a risk profile that those "banks" define and Stripe and others must keep all their clients within the profile. So if you don't fit within that risk profile you are out of luck. Generally the risk profiles are the same at almost all clearing houses so you won't find a lot of differences, unless the company also has worked within your countries banking system too.
Paypal works differently than a traditional merchant gateway from my understanding as well they have worked through issues in other countries to be compliant letting them process credit card transactions natively in those locations. But with that comes some of the crazy things they do, like locking up your funds for months and trickling them out to you if your volume changes too rapidly, amongst other reasons.
Good luck.