I understand that patents are a "negative right," but...
Constitution doesnot see it as a negative right it is given to promote and encourage innovation. But in fact you may be right the patent may give negative rights in case if patent owner is using evergreening strategy i.e., patenting a mere addition of a feature to already existing invention and blocking others entry.
Is it a reasonable assumption that patents aren't granted if they infringe on prior patents?
yes patent may be granted even if it infringe a prior patent that has a broad claim and such grant is supported by statue. The factors which would be generally considered are scope and content of prior patent, diffrences between the invention and prior art. other factors such as improvement over prior art or failure of prior art to disclose the feature claimed.
Is there any precedent where a product (that is a one-to-one implementation of its (valid) patent's blue prints) has been sued for infringement?
This do occur in pharma as the prior patent claims a broad group of compounds in form of Marukush groups and next patents are narrowed to the actual compound.
But the success for plaintiff cannot be guaranteed in such cases the classical example for me is Merck vs Gileads case where merck lost the case due to the unenforceability of two Merck patents covering a drug presently marketed as Sovaldi(r) to treat hepatitis C, sofosbuvir. and reversed a $200 million award.
where as the case is different in case of shire vs Fresenius involving drug icatibant where plaintiff won the case.
the success differs from case to case