It's totally, completely, and thankfully, false.
I had this discussion with my students tonight in classes. The claim that ice water is dangerous to dogs is simply not true. The ASPCA and other shelters use ice as a mentally stimulative tool for keeping dogs sane in kennels. Huskies eat ice to stay hydrated during running events (including the Iditrarod). Snopes has confirmed this is false, though I'd rather people talk to their veterinarian
That being said, it's incredibly sad that the woman in the story going "viral" had a horrible event, but one anecdotal circumstance does not an epidemic make. This also went around last year, and the year before.
Give your dog ice. The worst that could happen is brain freeze, unless they are suffering from heat exhaustion or heat stroke. Then call your vet because in those cases, ice, or any drastic temperature change, can be a shock to the system.
The Internet is great for so many things, but check your sources. I'm saying this as a blogger: blogs aren't always correct. Go to a reputable source.