This is actually a really good point. I can't find it now, but there's an article floating around somewhere about a government employee in some small town accusing Apache or Debian or some project of being "hackers" because his web server broke and was showing the default "congrats it works!" page instead of the town web site.
An ex-boss accused me of hacking and embezzlement(!) when he discovered he was paying £10/month for DNS services a few years back. It was something in place from years before I even started!
He also flipped out over firewall issues on his new Macbook (the site is down and taken the internet with it!) and problems with his ISP (some weird adult filter).
Point is, some people expect a site to be a single atomic thing with no dependencies or connections between. Through anything "unusual" in there and confusion and chaos reigns. My ex-boss was somewhat extreme I admit, but I've experienced it to a lesser degree many many times.
What if your customer sees Heroku's name, and gets confused?
She starts asking questions like: Who is on the other end? Am I in business with X or with Heroku? Who should i call?