Racehorses are rarely if ever cinched up quickly and with brute force as far as the girth will go. Usually they are saddled in the stall ahead of time and stand for a bit waiting for the rider to get off the current horse and get on them. When they are saddled in the stall the girth is not tight at all, simply snug enough so the tack doesn't fall off while they stand or walk in their stall and wait. Once they are taken out of the stall and the rider checks their equiptment (saddle and bridle) the rider will tighten the girth before mounting and then gradually tighten it more and more as they walk to the track. You might see some ignorant behavior at smaller/cheaper tracks where you have less skilled or completely unskilled "horseman" (I use this term extremely loosely as I know one trainer who hires bums out from under bridges to groom for him...rolleyes). But at the bigger/nicer tracks where the horses are worth big bucks, they tend to have better people and don't put up with the horses being mistreated or even treated roughly. Of course there is an exception to every rule and you are bound to find a few morons with nice horses who still manage to win races and no one can figure out why they win and why any owner in their right mind would give them a horse in the first place. Lol
All that having been said, sometimes a horse is just sensitive and it has nothing to do with how they were handled. My 8 yr old is a little girthy and is a retired racehorse, but he doesn't really complain much, but I also still saddle like I do babies at the track....put it on, walk them out then tighten and tighten again after mounting, so he is used to the routine. My 20 yr old who is also a retired racehorse is extremely girthy, but then he also hates being brushed! He is very thin skinned and sensitive, and will pin his ears and act like he's going to bite. He never bites me, but I am mom, but he will take a chunk out of strangers if he is so inclined. Again, I don't think it has anything to do with how he was handled as my brother was the asst trainer for the guy who had him and my brother also groomed and galloped this horse so I know he was handled well and with good hands. He simply has sensitive skin and hates the process of getting ready, it is not fun for him. But once he is saddled he is fine. He is even fine with me tightening the girth once on him, he just hates it while I am on the ground. I guess he stops caring once I am on his back as then he knows we are going to go have fun. :) But he always complains about brushing, so I keep it to a minimum and bathe him as much as possible.
As far as what to do, I would just put it on and then walk her a few steps or in a circle, then tighten it again, but just snug. Then once you get on, tighten it again. Little by little, not all at once. If she still protests, you may just have to learn to ignore it and go about your business, she may always complain a little. Just try to make it as pleasant as possible.