This sounds like a tough situation, and I can understand why you're feeling upset. It’s never easy when your child is left out, especially when you’ve done your best to foster good relationships in your neighborhood. Your instincts to clarify the situation with the other parent are understandable, but I think it's important to approach it thoughtfully, keeping both your son's feelings and the bigger picture in mind. Here's how I would suggest you handle it:

First, some things to consider:
Your son’s feelings: He’s understandably hurt, and acknowledging that feeling is important. Let him know that it’s okay to feel upset and that sometimes social situations can be confusing.
The other kid's intentions: It’s possible there’s a misunderstanding or something that the birthday child’s parents didn’t communicate well. While it might seem like an intentional slight, there could be an innocent reason (or even a simple oversight) behind it.
The parent dynamic: You mentioned your wife’s thoughts about the mother possibly being a narcissist, which could suggest there’s a history of manipulative behavior. If that's the case, confronting her directly may not be the most productive or healthy way forward.
What you might say if you reach out to the dad:
If you do decide to reach out, I’d recommend being calm, direct, and non-confrontational. Here’s an example of how you might phrase it:

Example Text or Message: “Hi [Dad's Name],

I hope you’re doing well. I just wanted to check in about the birthday party tomorrow. My son came home a little upset today after the boys were at our house and found out that he wasn’t invited to the paintball event. He was told it was because of his finger, but it doesn’t seem like a big issue, and it’s left him feeling a bit confused and hurt, especially since he’s so close with [birthday kid] and the other boys.

I just wanted to reach out to better understand what happened, as I’m sure this wasn’t intentional. We’ve always tried to keep the lines of communication open, especially when it comes to the kids, and I thought it might be good to touch base directly.

Thanks for your time, and I hope we can sort it out.

Best,
[Your Name]”

Why this approach?
Keeps the tone neutral: You’re asking for clarity rather than accusing or making assumptions.
Shows empathy: You acknowledge your son’s feelings, but you don’t place blame or escalate the situation.
Gives them space to explain: There might be something you don’t know—this way, you're giving the parent a chance to explain, which can prevent any unnecessary confrontation.
Other thoughts:
Managing expectations: Prepare yourself for the possibility that you might not get the resolution you hope for. If this becomes a recurring issue, it might require a bigger conversation about boundaries and expectations with your neighbors.
Modeling resilience for your son: While you can’t control other people’s actions, how you respond will set an example for your son. Reinforcing that sometimes people make mistakes or act in ways we don’t expect will help him cope with this disappointment in a healthy way.
Final considerations:
Your wife’s point about not reaching out may stem from a desire to avoid unnecessary drama, especially if the other parents’ behavior has been problematic in the past. If you think that reaching out will cause more stress than resolution, it might be worth taking a step back and letting it go this time. However, if you feel like addressing the issue directly will help clear the air, then it’s okay to ask for clarification.

The key thing is, whatever the outcome, continuing to support your son and validating his feelings will help him navigate this tricky social situation.