I've had these issues myself, and know the "stereotype comes from somewhere", but...does anyone work off of anything besides anecdata in discussion re: the stats behind this position? It's very defeatist.
I worked in email deliverability for years. It's absolutely true. Mainly because the big providers work together to make sure that their mail is successfully delivered to each other, and they also work with big corporations.
I was working on it when I worked for ebay and PayPal. I was working with Yahoo (who was big at the time) on what became DKIM, which was created to make sure that Yahoo mail was delivered successfully and that ebay and PayPal mail would be delivered successfully, among lots of other big corps.
Sure, anyone can use those technologies, but only the big players run interoperability tests on a regular basis, and provide reporting to each other, and other big corps.