Glucose uptake is not inhibited in type 2 diabetes and insulin resistance:

https://www.jci.org/articles/view/116226

https://academic.oup.com/bja/article/85/1/69/263650

https://www.ncbi.nlm.nih.gov/pubmed/11431133

https://www.jci.org/articles/view/111258

Glucose oxidation is inhibited in type 2 diabetes and insulin resistance:

https://www.jci.org/articles/view/116226

https://www.ncbi.nlm.nih.gov/pubmed/9216960

https://www.ncbi.nlm.nih.gov/pubmed/17472434

http://science.sciencemag.org/content/300/5622/1140

https://academic.oup.com/edrv/article/25/5/807/2355272

Hepatic glucose production is responsible for fasting hyperglycemia in type 2 diabetes and insulin resistance, and insulin lowers fasting hyperglycemia in these conditions by inhibiting hepatic glucose production rather than increasing glucose uptake:

https://academic.oup.com/bja/article/85/1/69/263650

https://www.ncbi.nlm.nih.gov/pubmed/11431133

https://www.jci.org/articles/view/111258

Issues with low-carb and ketogenic diets:

https://jayfeldmanwellness.com/carbs-vs-fats-which-is-the-better-fuel/

https://jayfeldmanwellness.com/carbs-vs-fats-hormonal-effects/