Why are Rebel's denying they received Death Star plans in the begging of Episode IV even though Darth Vader seen one jump to hyperspace like a day before? Well, a CR90 Corvette is not exactly a unique ship to the Rebel Alliance. In fact, not only is it not a unique ship, it is fairly common. Saying you own a CR90 Corvette is like saying you own a Ford Mustang. Yeah you own one, but it is not the only one rolling around. That is probably a bad comparison, but you get the idea. CR90's can be privately owned by civilians, even the Empire used a few of them for ceremony purposes in the Imperial Senate. I have even read Legends material where the Hutts used them. It is because CR90's are made by Corellian Engineering Corporation. CEC is like the Honda Motor Company of Star Wars. Anyone can by ships from them.
Do not get me wrong, it is a decently armed ship for civilians, but most ships in Star Wars already are equipped with some for of defense. A CR90 is like any corvette one would expect in Star Wars: only good in starfighter defense. As I understand it, they are cheap, easy to fix, and can put up a fight against large numbers of starfighters. Which is probably why the Rebel Alliance purchased so many of them -- they were on a budget.
If I owned a CR90 and the Empire stormed down my ships air lock, I would have said "what is the meaning of this?", "you stormed my ship because it looks like one that left Scsrif?!", "search the ships computers, you will see they are not there." Because I would have already hidden them, ha! Then I would have said "Damn Imperial military! Now get off my ship!"
I think Leia was hoping she could get away with the fact she is flying something common, while playing the diplomatic immunity card.