As the comment above points out, that’s a huge exaggeration.
Thankfully, this has been explained many times in the forum and it’s pinned in the sticky threads.
It’s their responsibility to write code for the game. Their hosting is handled by Google these days.
Blizzard is not an internet service provider. They’ve never been responsible for latency issues, but supported them as a courtesy service in the past. Now they operate like most other game development companies—only offering troubleshooting steps via ticket and on their support documentation site.