Yes...a foreigner can be enrolled the Peruvian private insurance system but once you are enrolled, they require a "10 month waiting peroid".To get past this rule,just show that you have been in another health insurance policy for the past year and a half (proof of past insurance) and they should waver the 10 month rule.Remember in Peru,your passport number takes the place of their national ID card number which is used for insurance,creditcard charges etc.