I didn't go public so I can't really comment but I'm not sure what your doctor was getting at with that remark. I can't imagine what would be different about going through IVF in a public hospital vs a private one except that you maybe don't have to wait as long in a private hospital. Perhaps he was referring to the odds of you having a greater chance of success with some continuity of treatment. It sounds like he is talking about you having to wait for a while if you don't fit into the slot he is now offering you. Just my guess.

If that's the case, go for it.