Depending on when you are remembering, no you're not.
The LSs had fareboxes (photo - not mine -
here) at least some of the time, and as I remember them.
I am fairly sure the Red Arrow LSs were new with fareboxes rather than turnstiles, and I think the MBA's kept turnstiles until they were withdrawn (although I think I only travelled on one the once.) Although there was a brief overlap (not sure if each route was converted in one go or whether there was ever a mixed allocation on one route - at that time, they were spread out among a few garages rather than a single Red Arrow base) so anything is possible.
And some SMSs were moved on to Red Arrow routes around 1979/80 - I can find a few photographs of them in action, but can't see clearly if they had a farebox or not.
Around the time the LSs were introduced was when LT started pushing bus pass sales, and think there was initially an option to add a bus pass on to a train season ticket (it may have started with Underground seasons and extended to BR seasons, before 'Capitalcard' became a thing. At that time my father worked within walking distance of a Southern Region terminus, so didn't travel by bus in central London regularly enough to get one) so there would have been a need to allow passengers on to the Red Arrow routes without making a cash payment. I don't think the turnstiles had an arrangement where the driver could allow a free entry, as that could have been open to fiddling...