If bacterial resistance randomly occur, then why limit broad-spectrum antibiotic use?
You're correct, this is extremely relevant, and it's unfortunate that your medical education didn't include good instruction about evolution. 

You point to some very useful and interesting studies. I'm particularly fond of the studies that demonstrate the early existence of antibacterial resistance genes, e.g., in ancient permafrost.

Now to your question


  Is it a scientific fact that emergence of bacterial resistance through mutations is always random, i.e. in the sense that it is not a directed response to exposure of the population to that antibiotic?


I think the issue here is a conflation of two separate concepts. Mutation is one mechanism for producing variation. Mutation can be understood as a stochastic process, causing changes in the genome of an individual by chance. 

Evolution occurs because of existing variation. Evolution is not a stochastic process. It is a biased process, a change in the distribution of existing variation. 

The emergence of antibacterial resistance is evolution that results from selection acting on existing variation. Emergence here refers to emergence of a resistant variant within a population. Selective pressure (application of antibiotics) causes a predictable change in the frequency of genes that would allow reproduction in that environment, the frequency of existing resistance genes increases in the bacterial population.

Though there is evidence for important antibacterial resistance mutations pre-dating the use of antibiotics, this does not rule out the occurrence of spontaneous mutations, as demonstrated in the article you linked. The production of genetic variation by random mutation can be followed by a rapid increase in the frequency of a new genetic variation that is selected for in a given environment. This can be particularly likely in organisms with high error rates, short generation times, and large numbers of individuals. The spontaneous mutation isn't directed, as you say. It is random. The selection of that particular random mutation is directed, though.  Once the random mutation occured, then we can say the variation exists. Then selective pressure acts on existing variation, allowing evolution, a change in the frequency of the, in this case, gene for resistance.

Goodman &amp; Gilman, one of my go to pharmacology references, actually has an excellent discussion of these concepts as they relate to antibacterial resistance, in Ch. 48, under the subsection EMERGENCE. There is a good discussion of the various mechanisms of emergence, but this general statement is helpful:


  Mutations are not caused by drug exposure per se. They are random events that confer a survival advantage when drug is present. Any large population of drug susceptible bacteria is likely to contain rare mutants that are only slightly less susceptible than the parent. However, suboptimal dosing strategies lead to selective kill of the more susceptible population, which leaves the resistant isolates to flourish.