Should product marketers be "influencers" or "partners" in product roadmap decisions?

You’ve done an admirable job of describing the differences, however the reality can be a lot more nuanced. There are many situations in which I have felt strongly about adding something to the roadmap and have argued with PMs to get it built. In other instances I’ve played a more supporting role providing data points and customer feedback, all in order to help them make a decision. Good Product Marketers aren't going to be only an "influencer" or a "partner" - they are likely to be both at different times.

What matters the most is credibility. Do your Product peers see you as a product partner or a customer communications manager? If they see you as a peer you are likely to be able to both influence and debate over the roadmap.

So, how do you build credibility? The big areas areas to invest in are:

• A thorough understanding of the product (you should know it almost as well as the PM), 
• Insights into your target customer base (who they are, what they want, etc.),
• Data, data, and more data. If you can back up your point with a datapoint you’ll usually win most arguments

My best relationships with PMs have been when I can bring some tangible insight to the table that helps shape the decision making.

If you're doing your job right, both. I believe everything PMM does should end up in the product at some point. Marketing doesn't have to be external or disconnected from the product. If you have this in mind, you can take the vast amounts of knowledge and insights and turn it into your companies’ .next. This means that partnership with Product Management is essential. Being able to synthesize all of the touchpoints for your extended product management team is a key service to your organization. 

For example, PMM at VMware owns or contributes to the following body of work which directly impacts product vision and functionality:

360 customer feedback
Customer adoption and usage data
Customer feedback surveys
1:1 customer meetings
Beta design sessions
Customer events
Market research and competitive analysis
BI / biz ops reporting
Day 0 (net new), 1 (starts using the product) and 2 (how do i get the most out of the product) marketing and enablement

Sales enablement

AR & PR

Lead and demand generation
Promotions and gamification as long as it is done in a tasteful fashion
Consumption engagement tools i.e. Pendo for SaaS

Ideally, PMMs are influential partners. :) 

As PMMs, we represent the voice of the customer in product decisions – because we know our customers and their needs best through the work we do. When you have influence, PM will bring you closer to decision-making. Sometimes this starts as bouncing ideas off you vs formal integration into planning. With trust, I think the ideal scenario is where PMM is integrated into the planning process, just as PM integrates into the launch/GTM process.