No, it certainly doesn’t!
The overseas parent company can own the IP without impacting the eligibility of the RDTI.
All your company has to do is be aware of its international tax obligations and transfer pricing issues, especially when the parent holds the IP offshore.
Moreover, it is an eligibility criterion, a formal binding agreement structured and executed between the parent and subsidiary. This is done to clarify the relationship between the parties and the mechanisms. The Australian entity generates future income through this, corresponding with the risk it is undertaking through the R&D program.
Of course, this varies depending on the IP ownership status!
Again, this is a complex area of the RDTI and would warrant further future discussion involving your Foreign-based legal and tax advisors.