When I read the same bits of the manual, I note that the 'Request Data' refers to 'attached device', just as it does in the 'Transmit data' section. No indication that it will NOT send data if requested.
As for the implementation chart, YES, the LAPC does NOT 'send' Sysex, as in it does NOT originate any Sysex, but clearly any Sysex that comes in is passed through, so in effect it DOES send sysex.
Also, I have two versions of the DOS package, Dr T's, editor for the MT-32 (and also for the LAPC). When this prog is run, all the parameter details for the card appear for editing etc. My understanding is that this data is read from the card at that point. So the Dr T's prog must be sending a 'Request Data' and must be getting an answer. Or might it be doing it some other way?
If there's something wrong with the connection to the card, then the prog reports there is a problem, and does not have any data.
I know I've used Sysex to SEND banks of data to the Roland. Many of the patches I have were obtained as complete banks. I have a couple of varieties of the sending prog. I'll have to unearth all my bits of that type (from 20+ years ago) and check if there was a 'Receive' variant too. Certainly, I have a bank, which I assume was obtained via Sysex, of the standard settings of the card.
When you've tried a Request Data operation, what happened?
I'll check out the Quest Studios site, but I think I've been there a few times, got some midi files for certain games, and some of those files include new patches. I was very interested to read somewhere that Jan Hammer had done the music for (I think) Police Quest 4, and I got the midi files for that, and yes, there's Sysex embedded in the files including a number of new patches, some for sound effects, but others for definite instruments.
PS - After some checking - I've tried the Dr T's prog just now, and when I try to load parameters from MT-32 it seems it cannot. So you may be right, or the prog uses a specific ID which needs to be changed? I do have various Sysex progs, which I think I have used, and some of those refer to 'Request Data' as well. I'll need to check them.
Does the MT-32 say differently on it's Implementation Chart?