I think Vegeta is in a state of desperation, and he's coming undone to a degree. It's one thing to win against 1st Form Freeza, but to beat Transformed Freeza doesn't seem to make much sense. But it could be a less than 8k Goku and friends versus Nappa scenario. Perhaps there are other situations like this as well, Unweighted Goku/Piccolo vs Initial Raditz and so on.
I don't think Vegeta actually says they can beat Transformed Freeza, so I'd need to see the definitive quote, but he also doesn't expect Freeza to power-up much.
It's times like these that I can't help to think of Final Form Freeza getting such a paltry boost being illogical. 1st Form to 2nd Form Initial is at least 2x, my goodness, Final Form Freeza's arrival is portrayed as the most devastating thing to ever happen in the series. FF Freeza getting a power-up at least on par to 2nd Form Freeza seems in order.
Chapter: 295 (DBZ 101), P9.1-5
Vegeta: “We can win! If the 3 of us fight together, we’ll be able to win somehow or another! [ ] It seems that even Freeza hasn’t noticed…These two’s battle power is steadily rising…”
Chapter: 296 (DBZ 102), P2.1-3, P3.1
Context: still talking about Freeza’s transformations
Vegeta: “Don’t be scared, he’s bluffing…he won’t change that much.”
Freeza: “Oh, is that right? Look vee—eery closely then. This isn’t something you get to see very often. Even when I attacked Planet Vegeta, where the Saiyans lived, and fought with the king, I was able to win without any need to transform whatsoever…Vegeta…your father wasn’t anything special.”
He may not directly say that they can beat 2nd Form Freeza, but none of this makes sense if he thinks they can't.
"We can win!"
Then tells Freeza to transform.