At least some agencies charged with ensuring the safety of foods say not.
It is possible that these notions arise from studies into the effects on pesticide residues of washing and cooking of fruit. For example a 2006-2009 UK Study.
The report looked at how detectable levels of residues were affected by washing, peeling and cooking fruit. However in the summary of that report there is no suggestion that residual levels in unwashed fruit were actually unusual or harmful.
In western countries at least, National and international organisations set maximum residual levels (MRL) for pesticides and national and regional organisations perform regular tests to check levels on fruit and vegetables. MRLs are set at a level that young, old and pregnant women can eat daily for the whole of their lives without appreciable risk to their health.
You don't need to wash or peel fruit and vegetables that would not ordinarily be peeled before consumption (for example apples) because of pesticide residues, as no assumption is made that such foods are peeled when deciding whether a pesticide can be approved for use or setting a legal limit (maximum residue level, MRL).
A package of toxicological studies is carried out on all pesticides before they are approved for use in the European Union. These studies follow internationally agreed guidelines. Based on these studies, levels of exposure to the pesticide that pose no appreciable health risk are determined. Both long term and short term exposures to pesticides are considered during the safety assessment.
UK Food Safety Agency (FSA)
an 18 kg boy would have to eat 534 apples every day of his life to exceed a residue level that is not dangerous to laboratory animals. And an 18 kg girl would have to eat 13,636 kg of carrots every day of her life to exceed such a level.
European Crop Protection Agency
The case study linked in the question is from China. This country has suffered from several high-profile food scares which some have attributed to corruption. Ref
For example, some Chinese mainland mothers still prefer to buy milk-powder from Hong Kong (some brands in HK are imported from western europe). Ref
HK testing suggests that food safety standards there are good. Ref