Whilst not contradicting Sally-Anne (or Bucks), perhaps there is a misunderstanding here?
For some grammars it is true that you are very unlikely to get a place unless you put them first choice. This is not because the schools disregard second choice, but because they fill up with children who pass, live in catchment and put it first choice, leaving few, if any places, for those who put it second.
I see what you are getting at, but here in Bucks
(and we are on the Bucks section!) the system does not take any account of where a school is placed on the preference list. Let me give you an example:
A parent applies for two schools - to keep it simple, both are catchment schools. The preferred school A is 8 miles from home. Choice B is 2 miles from home. Again, to keep it simple, it so happens that both schools are only able to take children who live up to 5 miles away from the school in each case.
School A can only take children up to 5 miles from the school gates, so the child does not gain a place there. However, the child gains a place at School B because they are only 2 miles away from it, and well within the allocation distance. The child gains a place ahead of someone who put School B as their first choice, but who lives 2.1 miles from the school. The allocation takes no account at all of where the school was ranked on the preference list
This is a much simplified example - there are sibling rules, Special Needs, catchment areas, etc, that muddy the waters, but I want to make clear that in Bucks it makes no difference at all where the school is listed on the preference list.
It is a tricky business untangling these rules, but it is extremely important that Bucks parents understand that they must always, always put the first preference school first, regardless of how unlikely it seems that they might get a place. Nice surprises have been known to happen!