I wonder if there is another factor involved as well, which is that this DD is number five, and maybe part of the attraction is that she will not be number five in the grammar school, she'll be number 1, and charting a different path.
How difficult would it be, if she sat for the grammar school, got in, and then decided it wasn't for her, to move to the comp? I would have thought not so hard if she still has the sibling benefit, how long until DD4 is through?
If that is the case, and in fact, she would have a pretty good chance of moving to the comp if things weren't so great, then I would suggest you back her and let her try:
a) you will have a fall back;
b) you will convey to her that you support her and her dreams (even if you don't think they are necessarily the best ones).
If she doesn't get in, then that is sorted (assuming you give her the kind of backing that she thinks is reasonable, i.e. comparable with her friends, or at least most of them, so she doesn't feel disadvantaged.)
If she does get in, then you can always point out to her if she is unhappy that she can transfer, and if she does decide to do that, then next time she is likely to take your views more seriously. On the other hand if she is happy, then you have clearly done the right thing and let her choose the option that is best for her. Choosing your own path is a big part of having the confidence to face the future, and can be more valuable than all the extra curricular interests, which can always be done outside (and if she then decides they are more important, moving to the comp can come back on the radar).
If you don't support her - there is the risk that anything that goes wrong at the comp will be laid at your door ("if only you had let me sit for the grammar school ...").
Seems to me that there is relatively little harm in letting her try, and quite a lot in telling her she can't.