My recruitment experience was similar to kaylasdad99’s. Although I did not join (the reasons are not relevant to the discussion), I was told that I did well on the ASVAB and what I qualified for. Like kaylasdad99, this was the Navy and was a few decades ago (1976). (Maybe in the decades that have passed, recruiting has become very deceptive or the Navy has the most honest recrutment policy).
As far as medical conditions, you are only given the most fundamental physical examination. The military couldn’t possibly give everyone a full medical workup as it would be too expensive and time-consuming. I’m guessing that basic training would “weed out” those with severe medical problems. Here’s a good example. Dan Rather had rheumatic fever as a child which caused some damage to his heart. Anyway, he decided to join the Marines but his medical problems became evident at basic training, and he was sent back home.
So, some people could fool the doctors but if a condition is bad enough, basic training will certainly make that fact more apparent.