One of the more arcane (but nearly universal) shibboleths of the copy-editing profession is the knowledge that that thing that everybody else calls a podium is actually a lectern.
It's hard to argue with the pod-/ped-* root, but, as I keep saying, please use your brain and not the search-and-replace function. OK, fine, a politician doesn't stand behind a podium to make a speech, but he or she most certainly could take the podium. (Who's to say such a reference is necessarily to the thing the speaker is standing behind, as opposed to the thing the politician is standing on?) Of course, you have to make sure the context is a rally, or something of that sort, rather than the White House press room, where the lectern simply stands on the floor, but if you're going to get all eggheady about what podium means, you should stick around in that frame of mind and acknowledge that it does mean something, and you should realize that there are plenty of cases in which either word would work.
*One of my favorite stupid everyday jokes goes something like: "We're going to be walking a lot, and we'll want to know how far, so don't forget to bring your pedophile!"