The gamma-ray emission in broad-line blazars is generally explained as inverse Compton ( IC ) radiation of relativistic electrons in the jet scattering optical-UV photons from the Broad Line Region ( BLR ) , the so-called BLR External Compton scenario . We test this scenario on the Fermi gamma-ray spectra of 106 broad-line blazars detected with the highest significance or largest BLR , by looking for cut-off signatures at high energies compatible with \gamma - \gamma interactions with BLR photons . We do not find evidence for the expected BLR absorption . For 2/3 of the sources , we can exclude any significant absorption ( \tau _ { max } < 1 ) , while for the remaining 1/3 the possible absorption is constrained to be 1.5–2 orders of magnitude lower than expected . This result holds also dividing the spectra in high and low-flux states , and for powerful blazars with large BLR . Only 1 object out of 10 seems compatible with substantial attenuation ( \tau _ { max } > 5 ) . We conclude that for 9 out of 10 objects , the jet does not interact with BLR photons . Gamma-rays seem either produced outside the BLR most of the time , or the BLR is \sim 100 \times larger than given by reverberation mapping . This means that i ) External Compton on BLR photons is disfavoured as the main gamma-ray mechanism , vs IC on IR photons from the torus or synchrotron self-Compton ; ii ) the Fermi gamma-ray spectrum is mostly intrinsic , determined by the interaction of the particle distribution with the seed-photons spectrum ; iii ) without suppression by the BLR , broad-line blazars can become copious emitters above 100 GeV , as demonstrated by 3C 454.3 . We expect the CTA sky to be much richer of broad-line blazars than previously thought .