Yes. One of the reasons I moved to my current home is that I can get all the way to the town centre and half the way to my doctor's on decent cycleways. Still not perfect, but a hell of a lot more fun than riding miles of narrow 40mph roads with a stream of motorists following. I'm pretty stubborn and have a fair brass neck, but I'd tire of doing that every day.
You probably heard that because a certain type of anti-cycleway cycling advocate likes to say such things. There's not really much evidence for it. Or against it, either, though. Having enough cycleways of any consistent standard to have enough incidents to make any useful generalisations has been pretty unusual until recently. I'll try to summarise what I remember:
There's a couple of half-cock analyses by John Franklin which claimed Milton Keynes's cycleways were more dangerous than the roads, but drilling deeper found (if I remember correctly) that he'd lumped all types of cycleways in together, from the bendy driveway-crossing residential ones to the much safer "grid ways", and he counted any crashes at a junction as for the cycleway not the road, plus he'd not adjusted for the types of cyclists: I lived there during the study time and it was mainly the fast roadies who still rode on roads — so experienced riders probably less likely to crash, but probably in bunches and at higher speeds when they do, mitigated by gloves, glasses and maybe other protective gear — with the rest of us using the adjacent redways, including the annoying underpasses swapping from one side of the road to the other.
There's also an oft-quoted study from about 1990 which was something to do with Lund University, looking at 1980s roadside cycleways somewhere, which claimed a 3x increase in danger for with-flow cycleways across side roads up to 11x for contra-flow at a major crossroads. That's the sort of study where the devil is probably in the detail, but there's no indication of assessing it for cycleway width, set back into the road signs, markings or kerbs or posts or whatever. It's contradicted by a recent study of the London CS routes, which found no significant difference, but that may also be down to a "safety in numbers" effect from attracting/concentrating cyclists onto the CS routes, or the small difference in speed (if any) between motorists and cyclists in London: it's difficult to left-hook someone if you're not going fast enough to pass them.
So, in short: it's complicated and both have studies to support them, but the older ones are very weak. Personally, I suspect it depends very much on the design of each cycleway. After all, a riverside cycleway with no roads crossing it is unlikely to have many cyclists left-hooked. A cycleway-carriageway junction with good intervisibility won't have many cyclists riding out in front of motorists who blatantly won't stop (no matter what the markings suggest) and will have more motorists see the cyclists approaching and hesitate to run them over while looking them in the eye! This is why we need good standards for common situations and a body like Active Travel England to actually enforce them!