if using Braintree would lead to problems like the ones mentioned by OP, what are the alternatives, in US and elsewhere, square cash?
Lots there and to be fair there a lot of other providers not even listed on that wikipedia page. Actually a few big ones that I have worked are not on there: Vindicia, PayEx, Paymill, etc
Here is a great piece by Danny Shader, CEO of PayNearMe. They are one of the most successful payments startups in recent history. You should give it a read: http://venturebeat.com/2015/02/17/so-you-want-to-start-a-pay...
But not one I would recommend. As you would spend too much of your time on your payment solution than your business. Continually trying to detect fraud, recovering from devastating fraud that has already happened, dealing with volumes of chargebacks, hiring a lot of customer service people, wasting time on edge cases, accepting customers from different countries, dealign with legal from different countries etc.
If only a niche business for local customers, with low volume, then fine. Not for nationwide, definitely not for international, and not for big volumes.