Meriel Buchanan wrote an account of the circumstances surrounding Elisabeth's death. Of course, she wasn't in Poland, but because of her father's position in Hesse and later in Russia, she knew Ducky and Ernie quite well. I think her mother was quite a good friend of Ducky's during her Darmstadt years. Anyway -- in MB's there doesn't seem to have been any rancor from Ducky over "not being called in time."
And Miss Eagar herself -- who WAS there at Elizabeth's bedside -- left an extensive memoir of the time, including the fact that no-one knew quite what was the matter with Elizabeth. She woke up the morning after Olga's birthday with a sore throat, but soon felt better. So she got up and dressed, and then felt ill again. So the doctor was called, and nothing more than the effects of the previous day's excitement was suspected. So she spent the day in bed, and seemed fine when her father and Alexandra came to see her in the evening. So the grown-ups went out to see a play. It was only on their return that things took a turn for the worse: The theater party went to see the children and visited for a while. Elizabeth was standing on her bed, and then suddenly fell unconscious -- this was when it became obvious that something more serious than excitement was going on. Elizabeth received caffeine injections to revive her, and a local specialist was called in. It was in the very early hours of the morning that Ducky was sent for -- allegedly, according to Miss Eagar, after Elizabeth asked for her, though this might be a piece of dramatic embroidery on Miss Eagar's part because she claims that Elizabeth knew she was dying -- and the telegram reached her at breakfast. So there was no delay in sending for Ducky. Not more than three or four hours could have passed from the return of the theater party and the sending of the telegram, which may itself have been delayed here and there, because some telegraph offices closed overnight.