This doesn't fit your question exactly since you seem to be looking for anecdotal evidence of the opposite. However it is an example of the limiting effect of high utilization.
Back at the tail end of 2012 I had very high utilization. I don't recall the exact figure but it was over 60% and I had been balance chased on at least one card because my utilization had been high for months. I applied for a Chase Slate so I could do a BT. I was approved but I received a $2K limit and the highest APR offered.
After that I managed to educate myself a bit better and I was in the position to drop my utilization to well under 10%. Again, I don't recall the exact figure. I closed the Slate because it was pretty much useless to me.
In 2013 -- 6 months after the Slate approval -- I applied for a UMPE and then a CSP the following day. Both were instantly approved for $25K limits each. Neither of those cards have a range of APR's offered but I applied for a BCP on the same day as the UMPE. It was also instantly approved -- only $12,400 but they bumped it to $25K at my request on day 61. While it didn't get the lowest APR possible it did get 14.99%.
My income and the other factors did not drastically change in those 6 months. Just utilization. Dropping it enabled me to increase my total limits nearly tenfold. Granted, that's because the rest of my credit was strong but high utilization was preventing me from making any progress.
It's not that creditors won't touch anyone with high utilization -- though more conservative creditors may not. It's certainly possible to get approvals with high utilization but it can be severely limiting as well as trigger adverse action if prolonged. Utilization definitely plays a significant role in credit scoring and assessment. For FICO it's the second most important factor behind Payment History.http://www.myfico.com/crediteducation/whatsinyourscore.aspx
I wouldn't recommend anyone assuming that their credit is in good shape for applications, CLI requests, APR reduction requests, etc if Payment History and/or Utilization aren't in good shape.