Keep in mind the script was from a top-shelf writer who worked on it for ages. It's established earlier in the film that the crew think it's completely plausible a computer dating service would set the two of them up.

"...Fellas. Fellas, look at this man's trash. He's not looking for "buff." The man who folded this tube of Crest...is looking for someone...meticulous. Refined. Anal. ...What?"

I think Cosmo's comment - note he's extremely vain, how he dresses, his office is practically a modern art gallery, he's got the organization's Cray sitting on display, etc - just further shows how vain he is, thinking someone as attractive as Liz couldn't possibly be a good match for a nerd like Werner, when it's established that they're actually quite alike/compatible.

One could imagine that Liz also obeys all speed limits and comes to complete stops at every stop sign...

I agree, and would add:

Cosmo has been in prison for a long time. His perception of dating service implications are unlikely to be contemporary.

He knew he had something Martin wanted. He knew what Martin and his partners did for a living. There was already the suspected breach, and finding Werner’s card in his office settled that briefly. When the mere mention of a computer came up in this scenario, Cosmo reconsidered how likely it was to be a simple misunderstanding versus his former close friend being involved.

Minor correction: I don't think they found Werner's card in his office. There just didn't seem to be anything amiss in there when they checked. As Werner said, "Well, uh, everything seems to be in order."

You’re right. Around 1:55:20 ish they don’t find his card left on a desk. and Werner just says everything appears to be in order.