They recently introduced blood glucose monitoring for BLS providers in my area, but many services have not completed the roll out for the protocol yet. I think that part of the reason why many areas do not give blood glucose monitoring to their basic providers is that it's not going to change the course of your treatment at all really. If someone's concious and altered, you can try to give oral glucose and see if the condition resolves. I know the argument that's glucose can increase intracranical pressure if the problem turns out to be a stroke, but the amount of glucose we would give would have a minimal effect if any at all. If a patient is unresponsive, you should have ALS coming anyway (if available). Knowing a blood glucose level doesn't really effect any of your treatment modalities.
The other argument that I've heard is that most BLS providers aren't trained in using sharps, and are not trained in invasive procedures. While it's a minimally invasive skill, it does involve a needle puncturing the skin. People at home with diabetes are given instruction (or should be) by their healthcare provider as to when and how to use their equipment. So they've been "in serviced," however minimally it may have been.
As a paramedic I would tend to recheck someone's blood glucose using my glucometer even if a BLS provider had one for me when I got there. The reason for that is to ensure that their reading was accurate (I know when my glucometer was calibrated), and also so that I can have before and after readings from the same machine. That part could simply be me being how I am...but it's how I do things. If a basic wants to check a blood glucose level, go ahead. It doesn't effect treatment though within the BLS scope for the areas I work.
Shane
NREMT-P