Things to think about before you call someone "Bad"

[Vidu]

So if the bad run is all a person ever saw of me, they can tell me that run was shit, and I will agree. However if they want to tell me that this one messed up snapshot enables them to call me a bad player in general, I disagree.

I both agree and disagree with you to an extend - I very much agree what you said about your situation. Mistakes happen, we should all be aware of that, things can distract you (I once wiped a Titan EX-party because I had a 30second long sneeze attack during hayfever season, everyone actually laughed about that) and so on.
Actually noticing that yourself and excusing yourself from the party is the right thing to do here and I believe it will leave a more positive impression overall than a negative one. You're showing/telling the group "I actually know better, today is just not my day". I would expect everyone being able to relate to that.

On the other hand, and thats probably not what you described anymore, but to make this a broader statment: Lets say, someone messes up mechanics in Suzaku EX, while also messing up basic job-functions. Like a RDM hardcasting, a bard not using songs/dots (and yes, I've seen that far to often in Ex-primals partys by now), a tank using all cooldowns at once, a healer not casting a single dps-skill even with enough downtime... all those things that are basic, underlying mechanics that should be reasonably expected from someone at level 70, specially when trying their hands on an Ex-primal. In those cases a snapshot can very well enable someone to "judge" that person fairly.
Sure, even then, you can argue that someone can missclick or forget their song once, because they're distracted, but if it happens frequently over the duration of the fight, excusing it as "accident" doesnt really work anymore and shows to me a fundamental lack of understanding and skill.

Again: The second case is probably not the case for you and I want to express again that I dont mean to imply that!
I just wanted to point out that
...yes, judging a players skill only based on the encounter specific mechanics might not be enterily accurate.
...but during that encounter you'll also see them playing their job and you can judge their skill on that.

You can be both bad at Suzaku EX and your job - or simply be bad at Suzaku EX (in that specific moment - either because you dont know the fight or because your cat just jumped into your lap).
And a good player will notice the difference and react accordingly, if at all.

Edit:
I would consider three "stages" of "being bad" right now:
1) Being bad at a specific fight (but capable of playing your job and reading mechanics in general) - easy, you're just in need of more practise, stay out of partys that dont match your skill-level, like farm-partys and depending on your knowledge maybe clear/kill-parties.
2) Being bad at your job - this is where it gets difficult, because this will show in all content and after a certain point (for me personally thats around Brayflox, but at least level 50 and definitly level 70) its not acceptable anymore if you cant perform your basic job-functiony. I dont care how you fix, but until you know how to play your job, you should stay out of (endgame)-group-content (with strangers). Dummies, playing with friends, running Sastasha again... dont care.
3) being bad in general - by that I mainly mean someones attitude. Anyone in category 1 or 2 can save themself in my book by displaying a good atittude, which involves taking (polite) advice, asking for advice, informing the group of any struggles or about them being new, apologising for mistakes... but if someone pulls the "I play how I want, you dont pay my sub!"-card, I'd label them as "bad in general, not worth bothering with"... and kick them.