Ok, The book says that the every character gets the "Universal standard kit". Which I note does not include a lasgun of full body flak armor. I would certainly give each specialist this "Standard" equipment. However, Regimental doctrines are what give different main weapons, armor, grenades and other such. Since specialists are not part of the regiment but are rather on loan, they would not get "Doctrine specific gear". Instead, They would get their specialist gear. Thus our Psyker attached to a Cadian line infantry regiment would have a flak vest and a Laspistol and numerous other insundiary survival gear but he will NOT have full body flak armor or a Lasgun any more than he'll have a heavy bolter or a Leman Russ tank! Specialists by their nature are NOT part of the standard regimental organization. Commissars hold no formal command rank nor are Engineseers subjected to being "repurposed" as infantrymen. They are all separate and then "Shoehorned" into the regiment as the need arises. While they have many of their own special benefits and abilities that's why they are there in the first place. The Idea that the munitorium does not care would more likely cut in the direction of the cheaper lesser gear than the better. For example: Psyker: Good morning! I'm new to the regiment and I'm checking in today. Munitorium adept: "Of course you are!" "Here is the list of survival gear you can draw from the back here. Your Las pistol and Flakvest will be issued from the armory". Psyker: "But everyone else is carrying Lasguns! Don't you want me to able to contribute to the regiment?" Muntorium adept: "You're a witch and I don't give a grox poo if you survive until tomorrow! This is what the sheet says you get and that's what you'll get! Move along or I'll have your minder shoot you now and save any of the REAL soldier's the trouble! Oh, and have a nice day!". You get my point.
So by this logic, a psyker or commissar in a rough rider regiment doesn't get a horse or equivalent form of transportation? Attacthed to a armored regiment? To bad, you don't get to ride in the tank cause you're only on loan... you have to walk. You're in a recon regiment that has chameleon? No cloak for you mister commissar. You're in a drop regiment, well too bad, I hope you can fly cause you don't get the standard kit.
The main thing is this, People keep saying there is no reason to give them standard kit because they are "on loan," but the real point is that there is also no reason NOT to. Nothing is gained by not giving the psyker a lasgun or full guard flak armor if he is in a line regiment... in fact all you are doing is hurting the player, he has less armor, a weaker weapon (and is missing other stuff to, like a chameleon cloak by the logic of most people here it seems), and has to waste time and dice rolls getting what is supposed to, by definition, be standard.
Let's quote the book here, page 75: "Support Specialists are elite members of the Imperial Guard who possess advanced training or unique natural talents.... No matter their rank or position withing the Imperial Guard, theses specialists' first priority is the same as the rank-and-file Guardsmen with whom they serve..." This whole section indicates that they are not even on loan to the guard, they are party of the Guard, and nothing in this section leads to them not getting the same equipment as everyone they serve with. Still have trouble, read the black box on page 58, I'll let you see one line, "...Support Specialists characters gain all the benefits and abilities of the Home World of the regiment they are serving alongside..." if they gain the benefit for being from a world they aren't from, then why would they not get the kit that is given out to all they squad mates on the battle field?
And as the final nail in the coffin, I would think, on if they get the kit of not... page 164: "Furthermore, some characters may be issued standard kit that they never actually use. For example, every character is issued his regiment's standard model of lasgun. This includes specialists who might always wield another weapon..." The fact that is says character here and not guardsman, contextually means all characters, regardless of specialty.
Now GM's and players can decide to ignore this; that is their right, but at least be honest that that is what you are doing. There is no reason, in the game or lore, not to give them full kit.
Hmmm... OW pg. 68 is where I got my info. Whereas your information is ALSO accurate from page 164. These are apparently in conflict. I would issue the Las Pistol as standard you would issue the Lasgun. I guess it's a matter of interpretation rather than RAW (Which are in this case, in conflict.) I would tend to want my PC's to look and feel about the same as they do in the TT game at least when they first start out but that's me. It would seem that either interpretation is acceptable and probably varies between regiments. I also don't understand why a regiment would issue a "Standard weapon" when the specialist has his own arguably better or more expensive gear issued. (The Commissar's bolt pistol is an example) which already replaces their "Main weapon". Specialist gear is intended to replace the standard gear according other points in the book (Too lazy to look up the page right now) so yeah, I've been ignoring that particular passage. As to mission specific gear their is already a mechanism for that. If a Commissar were being sent out with a recon regiment than I would include his Chameleon cloak as "mission gear" specifically for the Commissar. The same would be so for the Grav chute and of course said Commissar could ride in the Chimera or might even be assigned to "Command" a tank! They would just not be issued to those characters directly. As to your quote from the book on pg. 75: Members of the Imperial guard. Try telling that an Engineseer of the adeptus mechanicus! It won't work out well according to established fluff. This is also true of a Ministorium priest. Go ahead and tell him private, that he is a member of the Imperial guard and therefore must listen to all the shenanigans of politicking officers. Again, This member of the Ecclesiarchy is not going to take too kindly to that thought!