17 pages? There was a user shortly after the K-3 debuted who was very concerned about shutter lag for flash, but I don't remember any particular outcry.
https://www.pentaxforums.com/forums/172-pentax-k-3/242556-k-3-delay-when-using-flash.html
The above thread (15 pages) discussed the lag, but quickly degenerated into a general discussion of the weak points of Pentax flash across several models and then withered to a series of yes I have, no I don't posts. To the best of my knowledge the behavior was never addressed in firmware on the K-3. FWIW, I don't know that any reviewer of the camera detected this behavior or found it to be problematic. Some users in the above link were able to reproduce the OP's complaint and others not. In at least one case the lag was user error (red-eye reduction on). I am able to perceive a few millisecond lag on my K-3, but only in PTTL mode. Consensus on the other thread was that the lag was prior to the preflash and flash and was related to some unknown calculation of ambient exposure and/or communication with the flash itself though that explanation was not universally accepted. Whether other Pentax models at the time had similar behavior was not well established either.
To the best of my knowledge nobody did an automated timed test. Wrong...see below...
Based on the comments for the older thread and here, it seems that some users are more sensitive than others and in at least one case. My advice to the OP would be to report their concern to Ricoh/Pentax and perhaps start a new thread on Ricoh's official user forum. (Ricoh does not regularly monitor posts to this site.)
Edit: I reviewed my comments on the previous thread and forgot to note here that I was able to compare the lag on my K-3 to that on the K10D
I owned at the time and found the K10D to have a much longer lag.
Steve