Yes, all unis will support you for the PhD portion. Some will support you the entire time, while others will support you for the PhD and 3rd and 4th year.
I will be applying to DO/PhDs. As for the advice not to do it - don't listen. The fact is if you want to do a PhD, that means you want to do academic medicine, i.e, research. And a PhD matters. You won't be doing it at the same time, so it's not a matter of focus. You'll generally take 3-4 years off after your second year of med school and you'll do your thesis.
I love research and so that's what I'll be doing. It'll probably help you in landing a better residency - if you're going to be in academia, having a PhD is a definite plus, since you can bring in research $$.
However, one thing to understand is many DO/PhD programs are in health policy or something similar, rather than a pure science. PCOM for example has a DO/PhD, but it's not a science PhD. Whereas schools like OUCOM have pure science PhDs that you can get in conjuction with your DO. So just be aware of that, and apply widely. I hope to be seeing your around. IMO, the osteopathic profession needs more academic physicians.