In addition to the two rules (depending on natural pronunciation) of adding an apostrophe to a noun ending with the letter 's' here on OxforDictionaries, the apostrophe is not added to a noun that already has an apostrophe.
Having said this,
Wendy's product manager insisted...
will serve the purpose and is grammatical.
A couple of examples -
McDonald's chief executive Don Thompson defined under performing Australian and Japanese markets as weak and said the Illinois-based company was concentrating on 'stabilising' key priority markets in both Australia and Japan, as well as Germany and the U.S., reported the Sydney Morning Herald - from DailyMail.
The McDonald's parking lot is full of pickup trucks with fishing gear jutting from their beds, sleek hybrids with kayaks or mountain bikes racked to their roofs or tailgates and family vans packed with kids coming from soccer tournaments - from Tribune.
In that same interview, Wendy's chief marketing officer, Craig Bahner, noted that Wendy's customers widely request the pretzel bun for other products. Sure, it costs the customers 30 cents more, he said, but "we totally accommodate. We want them to have the product they want." - from USA Today
A Google search for 'Wendy's chief marketing officer' gives the result with the answer Craig S. Bahner.
A little note: I think when we talk about some authorities from some company, not putting an apostrophe is okay. In other words, when we talk about the designation, apostrophe is not mandatory to use. For instance, "Microsoft CEO said that..."; "IBM spokesperson added that..."; "McDonald's Marketing Manager agreed that...", and an article with the headline and an image caption from NYDailyNews which reads Former Microsoft CEO Steve Ballmer etc.