Let's break it down piece by piece.
"So we were dispatched for a weak woman on side of street. Got there. She was 79 and altered. Didn't know her address couldn't really answer any questions. Obtained vitals and bgl. Couldn't obtain BP because everytime cuff would inflate she would move arm and start crying. Tried to obtain it 3 times without an accurate reading."
All sounds right - you ruled out any trauma, went down the AMS pathway, ruled out hypo/hyperglycemia
"Perform stroke scale. Equal grip strength no droopage or slurred speech no arm drift."
To the best of your ability, identified no immediate indication of a CVA using CPSS (not that specific of a scale, but if you combine with age and BGL, it's not so far off from LAPSS, which is much higher specificity).
"Transport was only 5 min away. Called for als but they could not intercept."
If a stroke, not much ALS could do.
"Got to the hospital and told nurse I couldn't get a bp and that we performed the stroke test but didn't find anything besides the confusion. Apprently they got a bp reading of 220/110 and brought her to cat and she was having a stroke. So now the nurse is very upset. I'm also upset with my self as well."
Transport is the only BLS intervention indicated, as far as I can tell here. You can't get a BP - that happens! Did you try to palp one at least?
Don't be upset because the nurse is upset - she doesn't have the context of what you can/cannot do outside of the hospital. And you don't have CT - not like you could know! (If you get a follow-up on the patient, it might be interesting to see what kind of stroke it was. If a posterior stroke, my understanding is that traditional prehospital stroke scales aren't great at catching these.)
Also, as mentioned by others -- the BP alone in the setting of AMS is *not* solely indicative of a stroke, and shouldn't change your management in this case.