[citation][nom]banthracis[/nom]I don't know what doctors you go to, but the ones I go don't have google open during a consult to look up possible diagnosis for every symptom I give them.[/citation]
No... They don't look at google... They instead check their reference book in the back, they double check THAT in errata published for the reference... then they use their online tools to make sure... and then... AFTER ALL THAT... They still suggest you consider a second opinion on any major medical procedure or treatment.
School should be used to teach students to find information, give them the ability to recognize what information is needed, (EG. Formulas, possible causes for symptoms, ETC.) and finally apply the information that the profession needed to check anyways.
For the EMT example, their training is exceptionally good general care for common life threatening conditions. Your EMT won't be able to save you from anything more specific than poisoning.
As for the engineer example... Via the internet and online forums, (such as this one) any shmuck can get the resounding NO they need when they try planning something stupid (See me paying 3000 quid on an prebuilt w/o even an reasonable case.)