As evidence of how implausible it is that this is good advice, many objects that are part of the standard library (std::string, std::vector...) do provide constructors that allocate memory.
Standard library treats memory allocation as orthogonal by using allocator concept. Entire operation of the library handles all resource allocations via external interface, which falls in line with original advice. While operator new can be overloaded, the default versions do not pass in context in which they are called, suffering from typical global namespace issues.
When designing APIs, the biggest mistake is to internalize resource allocation. In C, allocator function should be provided. In C++, allocator. In Java or C#, factory interface. Dynamic languages do not suffer from this as much since any call can be mixed-in or modified at any point to insert cross-cut functionality.
The lesson here is rarely emphasized enough, but resource life cycle is absurdly complicated problem. By including it into some library or algorithm it creates such rigid design that it may be rendered useless for any further development, either through reuse or through feature changes. Resources here can range from memory to files but even to number of rows in database, number of URLs supported or lines in a file.
FactoryStrategyFactorySingletonProvider is somewhat of a joke in Java world. Admittedly, Java is a clumsy and verbose language, but the problem is real. Di/IoC is in many ways the worst of all worlds, but it emerged as only scalable (in terms of development) methodology. Key lesson is to decouple resource creation/allocation from business logic/rule engine. It really is that important as projects grow.
And as said, dynamic languages do not suffer from this problem, even though at surface they appear to be allocating objects left and right. Focus is on resource allocations and memory in most languages and problems isn't important enough. C and C++ tend to be used precisely for this reason, so memory should be treated as one of resources that needs to carefully managed.