Unfortunately, no. I'm the NA, and according to our ISP at this location, nothing is being blocked.
On further investigation, it appears that not everyone is having this issue. Not exactly sure what's going on, but I'm 70% certain it's not DH now.
I am very curious, though, why the tech support person I was speaking with would tell me to make such a drastic change in our infrastructure. Ah well, I'll chalk it up to a poorly trained support rep. Wouldn't be the first time.