Ok, kinda double posting, but I just went through and sort of verified it. When you select gang vehicles from your crib, it uses the gang_customization.xtbl file to see what it can select from (notably under the <gang_vehicles> section). It then IGNORES THE VARIANT FLAG! It assumes the vehicle given has a "saints" variant in the crib menu when you select a vehicle for a slot. If the vehicle does NOT have a saints variant, it shows an empty space where normally it would show the vehicle, as it tries to load the "saints" variant and fails. There's error-correction there and you can't select the vehicle as the variant "saints" is not found.
If it DOES have a "saints" variant, you can select it. HOWEVER in-game when it randomly spawns a s Saint in a gang-car, it goes and looks at the list of gang cars, picks one at random. It then proceeds to ALSO ignore the variant flag. Possibly, at least... In turn, it picks the standard variant, ignoring traffic weighting and such. And your gang member is spawned in a vehicle thusly. That is why it appears to NOT work.. it's working off the list of gang options you gave it, but as the variants shown are just the normal traffic variants anyways, they blend in. The best way to verify this is to add a vehicle that can't show up in traffic, like heli_fighter01 or heli_fighter02 (both of which are selectable as they have saints variants). You will eventually see them in Saints controlled areas, parked (the AI can't fly)... and they will be in generic black or grey or whatever the usual is for that vehicle.
When you use the phone to call Saints Backup... they do not use the gang-cars. You can verify this by changing the gang-cars, and then calling for backup.
I'll just say this was as "fun" to go and verify as you would guess. It's probably why it's never been noticed.. my personal random guess is they were having issues with selecting gang-cars (in the menu, or in spawning, or who knows what), and some programmer found that it was fixed by utterly ignoring the <variants> tag given in the selection. Or alternately, was just never saved in the first place. In turn, by the time shipdate hit it was either so low-priority or missed as a bug that cropped up that it was never changed in the engine. That means that the current method would be to add a "saints" variant to each and every vehicle you want to add. I can't seem to manage this myself, but others might have better luck. If you try that, see if you can add the vehicle to gang_customization.xtbl and MORESO select it as one. I'd suggest an uncommon vehicle like a tank, so when it spawns on the street you can pick it out quickly.
(edit) Did some looking. It appears to use the standard variant, and ignores weighting. Maybe. If the vehicle weighting isn't in the appropriate xtbl in root and is stored in say an str2 (a lot of the stuff in the game is duplicated, so why not this?) then I haven't tested that.(/edit)