IIRC, Stage III failures are responsible for a very high percentage of launch failures.
Well, let's see what statistics has to say.
I ignored failures of the payload, non-propulsion systems, or any failures where I could not identify which stage failed. Failures of staging mechanisms were rounded up to the higher stage. Flights with missing stages were still counted. All variants of each rocket family were included - Soyuz includes R7 launches, Thor/Delta includes Japanese licensed derivatives.
Soyuz: 25 first-stage failures, 18 second-stage failures, 29 third-stage failures
Proton: 9 first-stage failures, 11 second-stage failures, 17 third-stage failures
Ariane: 4 first-stage failures, 0 second-stage failures, 4 third-stage failures
Thor/Delta: 5 booster failures, 22 first-stage failures, 16 second-stage failures, 11 third-stage failures
Soyuz and Thor racked up a lot of early failures of the first stage, which seems attributable to simple inexperience (each had one failure from failing to fill the fuel tanks before launch). Even compensating for that, it seems the first stage is a dangerous stage, prone to failure.
However, your statement seems to bear out - the third stage does seem disproportionately dangerous. Oddly, it often seems to be control of the third stage that fails, not always the rocket itself.