Integrated with passive preamp section. Good or bad idea, or both ?

I think, active preamp is important, either separate or not.
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Audio Research makes them. I had one on loan to me, so I know first hand. I believe more companies do as well.

My old MF X-A1 as well as many of the Creek's as well as the Audio Refinement integrated.

And, this is just off the top of my tiny little pointed head.
The Ayre AX-7e integrated is a solid-state power amp mated with passive gain control and source selection. Love mine.
I thought the Gryphon Diablo 300 had a passive preamp section?
If I'm wrong, somebody please correct my statment.
"Integrated with passive preamp section: name one??Any... one."

I'll give you more than one; All Pass Labs integrateds.
If a passive control is built into a power amplifier or integrated amplifier, that's the best place it can be! By doing so, the designer is able to bypass most of the problems that make external passive controls problematic.

An early example of this is the Dynaco SCA-35 amplifier, which to this day is a great starter amplifier (of course, with refurbishment and updates). Essentially the only active circuits in it are the phono preamp and power amp sections- the volume, balance and tone controls were all passive and the power amp itself made up for their insertion losses.
IMHO, an integrated is the perfect spot for a passive pre.  You know the designer designed the amp section to work well with a passive pre, and you've decreased the parts count (and another interconnect) and therefore likely the overall expense to a great degree.  A passive pre with a separate amp gets a lot more sketchy in finding a good combination.  Maybe Ralph can chime in again and share what characteristics you need in an amp to be a good candidate for a passive pre.  My only thought is if the amp manufacturer also makes passive preamps, you're probably in good shape.  I'm thinking McCormack as an example.  But an integrated makes a lot of sense if it gives you the power you need and the sound you like. 
I recently put Burson Soloist preamp/headphone amp between the source and Redgum RGi120 integrated with passive preamp section, and everything is better with perhaps the slightest loss of resolution. And the Redgum doesn't even have power amp in input, I simply plugged additional interconnect into the line in. The sound was already quite good without the Burson, but the improvement was significant.
The preamp section in Gryphon Diablo´s are passive.
It depends on the sensitivity of the amplifier.  If the amplifier is extremely sensitive there is no need for gain from the preamp.

The Art Audio amps like the Diavolo utilize a passive preamp stage when converted to an integrated and our preamps offer switchable gain but when paired with our amps offer 0 dB.  

Alternatively, with a less sensitive amplifier, 6-12dB of gain may be required for it to sound right.