I don't know this school or people so I will refrain from making judgements about them. But...
If you want to learn a *specific style* and be part of its "family", then lineage is everything. Lineage has always been a part of these martial arts, as the tradition is important. You can't just decide to be part of a family, irregardless of skill. If someone is not telling you where they learned from, then that is a huge red flag to me. Especially in Chinese martial arts.. but then again, you still have to be careful -- there are several schools in my area whose masters lie about who they learned from to make themselves look more legit. So, not only do you have to know the lineage, it needs to be verifiable in some way..
Lineage matters even in martial arts that are considered "modern". You can't just decide that you are a black belt in BJJ. After earning it, you can receive it from someone authorized to give it to you..
But obviously lineage does not equal skill. Lineage means that you learned from someone who had access to the training methods and recognition as part of the family. But usually the most-skilled students are going to be well-known within the family or a branch of the family.. so once you find lineage, you should be able to follow the breadcrumbs to skill..
If you just want to learn to fight, defend yourself, exercise, or some such, then lineage obviously doesn't matter. But skill or teaching ability certainly does still matter here. In styles like boxing or wrestling, credibility is probably going to be based more on the past success of the coach or his students in the ring or on the mats.
But let's look at this logically:
If person A and person B claim to be doing the same style, but look completely different.. then maybe these are some options :
A. One of them is legit and the other is not.
B. Both of them are legit and someone along the lines of one or both changed or forgot what they learned (for better or worse).
C. Neither are legit.
Anyway...
What are you trying to get out of learning a martial art ?
At the end of the day, you need to decide if you are happy with the answers and the training you are getting. It reads to me like you are partially answering your own question, though..