You don't have to agree to anything you don't want to do. It's not essential to have the baby latch on immediately to have a successful breastfeeding experience.
However, if you want to, it can work and some studies show that if you do skin to skin and let the baby latch if they want to within the first hour of life it tends to increase the chances BF will be successful. It definitely can work like this. My first child didn't latch on during that hour. I sort of made a vague attempt to try but didn't really know what I was doing. I don't think I actually fed him for about 6 hours after he was born! We had that "golden hour" which he didn't BF during and then they wrapped him in clothes and a blanket to transfer us to the ward, he immediately fell asleep and so did I. I woke up 4 hours later in a total panic going help, wasn't I supposed to feed him?! But the midwives were really chilled about it and didn't think it was a problem. I also never used formula for him at all so it clearly didn't cause any problems.
With DS2 I had skin to skin for about twenty minutes, during which neither he or I made any attempt to latch and then they were concerned about his colour so they decided to check his oxygen again while he was on me and they weren't happy with it so they had to take him off to get some oxygen. Then when I heard he would be transferred, I asked if I could try to breastfeed before he went off in the ambulance and they said yes. So I sort of did what I vaguely remembered from DS1 and it worked, he did latch on and have a little bit of a feed. I think I was kind of hoping that would be enough to sustain him until I got over there but it took much longer for that to happen than I was expecting.
I have seen videos of newborns latching by themselves during the golden hour which is absolutely incredible to watch.
If you don't want skin to skin immediately after a section, just let them know.
If you do want skin to skin but feel alarmed at the prospect of anyone trying to "get" baby to latch (this would alarm me a bit actually!) then let them know you want skin to skin but no specific assistance with breastfeeding/latching at this time. Or just ask them to be hands off. They can support you verbally if it's something you'd like. I expect that it sounds more pressured than it really is though - probably just really badly worded! I think "We will try to get the baby to latch immediately" sounds quite alarming as though they will be all in there trying to make it happen ASAP which is neither breastfeeding nor baby friendly to be honest and would probably get in the way of you just looking at and meeting this tiny new person. So I expect that what they really mean is that you'll be offered skin to skin routinely, and in a position that allows the baby chance to latch if they want to (ie not with the baby's face right up to your face), which they may or may not. But either way - no harm in asking them to be hands off if you're concerned it might be a bit more "enthusiastic" than this.
Obsessed with BF can mean they have really good BF support or conversely it can mean that they are all talk and no trousers, which can be a really frustrating experience, but you won't know until you get there. Just don't be afraid to ask for support if you want/need it :)