Are gas giants actually rare? Kepler data suggests that the vast majority of planets are smaller than 4 Earth radii, with larger planets quickly becoming vanishingly scarce. Yet somehow, our own solar system harbours not just one, but two giant planets. This seems suspicious.

Are giant planets expected to be as rare as the Kepler data suggests? Or is there some bias inherent in the transit method that makes detecting giant planets more difficult? Is it perhaps the long orbital period of a planet that formed outside the frost line that has caused this apparent dearth of giant planets?
There is an observational bias and it is taken into account when you see inferences about planet frequency.

The methods to find planets are inherently biased towards finding large, close-in planets. Both the transit and doppler-based methods suffer from this bias.

The paper you reference takes into account this bias to arrive at the statistics you highlight in your question. Note however that the figure for Earth-sized planets is that 16.5% of stars have at least one such planet in an orbit with periods less than 85 days. There are no planets of any kind at all in our solar system that have periods less than 85 days. The figure quoted for Neptune-sized planets is 31% with orbital periods less than 245 days and there are no such objects in the solar system. Finally, the figure quoted for giant planets is that 5.2% of stars have a giant planet in an orbit with a period less than 418 days. Again, no such planet exists in the solar system.

You are correct that it should be unlikely for giant planets to form close to their parent star and this is one of the reasons that they are rarely found there. It is widely believed that the close-in gas giant planets that are seen, have migrated inwards from a formation site further out.

That said, it is perhaps true that our solar system is a little unusual.
Whilst we do not yet know what fraction of stars have gas giants in Saturn-like orbits (because observations have not been going on long enough), some work (e.g. Rowan et al. 2015) suggests that only $\sim 3$% of Sun-like stars have an analogue of Jupiter (periods of 5-15 years and masses of 0.3-3 times that of Jupiter).