The key for me here is whether advice proferred is asked for, or not.
In a scenario where I was seeing a health professional I'd expect them to proffer the BF advice first, then other advice as the situation might require.
In a playgroup or similar setting where a BF counsellor-type person was present in a professional capacity and identifiable as such and I wanted a chat/advice that would also be fine (although not if they continued to proffer advice and I said I didn't want it).
But what I think is unnecessary is for other women I'm barely acquainted with (eg other mums at a playgroup) to be worrying about whether I'm BF or not and attempting to broach it with me. And that's what I understood the OP to be about - not about midwives, counsellors or others offering advice that they're getting paid to disseminate for, as you say, public health reasons.
You're a humanist ... I'm a libertarian (although of the left wing variety, not the far right!). This doesn't sit very easily with parenting/being a mother of course, but I digress ...
What I find most interesting about this whole discussion is the question for those who want, for good reason, to promote BF, about how best to influence women to do so. We already mentioned advertising (posters and leaflets) - but actually this thread is about how face-to-face contact might be a better means of persuasion (coupled with access to proper advice etc).
IMO proactively offering advice after the event, when you're not sure it's wanted (as the OP stated) is in conflict with the personal liberties of the unwitting advisee (who in my case has made an informed choice, whether or not pro-BF-ers may like it) - at which point, if she's me she feels annoyed. Givers of advice may find more fertile ground than me of course - which is why the OP asks her question (should I risk upsetting someone by offering advice?).
If anyone in RL asks me (and I shall wait to be asked) for advice on BF etc in the future I shall say - give it a go, access the help and support that's available - and if you find you can't or don't want to do it that's fine - take another route because if you're happy the baby's happy.
This sort of 'do what you like' advice is hard for those who would like to see higher/longer rates of BF to combat - I expect those who get paid to promote BF in various ways have to think long and hard about how best to do it.
Anyway - that's enough makeshift political philosophy for one day!