The date doesn't seem to add up. If she had calculated it herself from the first date you both slept together, she would have had to tell you 9 months and 3 days. But that would not have been correct anyway as the pregnancy gets calculated from the beginning of your last period. It is true that cycle lengths can vary and that ovulation (the release of the egg, only after which it can be fertilized by sperm) can occur at different moments in the cycle than the expected midway point, which for most women is around the 14th day of a average 28 day monthly cycle. But if she had become pregnant in the cycle she was in when you slept togehter on 23rd may, she would have had to have been in that cycle for a few days at least, so she would be at least 10 weeks pregnant now.
The date would make sense if you took 23rd of may or the days thereafter (the sperm can survive in the vagina for a number of days and wait for the egg to be released) as moment of fertilization and calculated implantation, which occurs in the days thereafter, as the beginning of the pregnancy for 30 may. The doctors I know calculate the pregnancy from the first day of your last period though, that is the beginning of the growth process for the egg to be released.
Which country are you in? I ask this because whilst a woman herself is not unlikely to get mixed up and confused over the dates and the correct calculation herself, in the exitement of it all, doctors where I am tend not have this problem. But I wouldn't be able to say how doctors calculate pregnancy dates in other areas in the world.
There are the rare but sad cases where women invent a pregnancy for reasons that I can only imagine are psychological. The long term girlfriend of a guy I know pretended to be pregnant, to him, to his mother, their friends, everyone. He got worried when she didn't take him to any doctor's appointments. He found out in a very ardious process that she had never seen a doctor about it, the scans she had shown him were stolen god-knows-where and that the whole pregnancy was simply made up.
I am not saying this to scare you, just to be aware that sometimes very strange things can take place, so it's important not to ignore warning signs that tell you something might be wrong about the whole situation. If you ask she take you with her to a scan, and she agrees, that would be a very good sign. Then, at the scan, you can yourself ask the doctor what the actual stage of the pregnancy is. If she is happy to have that clarified with the doctor in front of you, again that would be a good sign.
If she doesn't let you take part in doctor's visits and if by her behavior you feel she is not telling you the truth about this, you can let her know in a very calm and non threatening way, after she is over 3 months pregnant, that you wish for a patenity test once the child is born. I say to wait for 3 months to be officially over because you wouldn't want her to ger very upset by your mistrust in a stage where a miscarriage is not uncommon to happen. Then you might feel guilty that you had caused the loss of the baby by upsetting her, a notion most probably misguided, but nevertheless you might feel that way. Or she might blame you, also not good.
Sorry it's become a long spaghetti answer - hope it helps. Good luck.