I would avoid the FIV personally, but would consider the FeLV if I walked any of my cats outside routinely. If you end up boarding your cats, the facility will let you know what their requirements are, but I doubt there would be any face-to-face contact between strange cats being boarded there.
As for the URI, it is possible Jengo picked something up at the vet's, or just the trauma of going to the vet's triggered a stress response which lowered his immune system causing a flare up of something he already has. For instance, the most common feline viral infection is rhinotracheitis or feline herpes and for 90+ percent of the cats who have it do not shed it but become lifelong carriers. It goes dormant until their immune system is lowered and they have symptoms again. Mycoplasma, a bacterial infection behaves similarly in some cats (and giardia as well, btw). Even in the dormant stage they can pass these types of infections to other cats, so again possible that Biz got the URI from Jengo. In reality there's really no way to know for sure, you just need to treat it and hope that takes care of it for good.
As for the URI, it is possible Jengo picked something up at the vet's, or just the trauma of going to the vet's triggered a stress response which lowered his immune system causing a flare up of something he already has. For instance, the most common feline viral infection is rhinotracheitis or feline herpes and for 90+ percent of the cats who have it do not shed it but become lifelong carriers. It goes dormant until their immune system is lowered and they have symptoms again. Mycoplasma, a bacterial infection behaves similarly in some cats (and giardia as well, btw). Even in the dormant stage they can pass these types of infections to other cats, so again possible that Biz got the URI from Jengo. In reality there's really no way to know for sure, you just need to treat it and hope that takes care of it for good.