Like you, the most invasive thing I had was to "cough", everything else was based on real world fitness, in fact getting my childhood asthma cleared involved pounding Woolwich common with a pti, nowt technical bout that.
As for a lumbar puncture, sounds like bullocks, reckon one or two recruits may have a previous illness, & the LP was recommended as a means to rule out nothing dormant in the system, but then capita, & any involved private medical practitioners cottoned on to the fact that they could quadruple their profit margins by insisting on a completely unnecessary dangerous medical procedure, thereby setting a precedent.
Was in wolf armouries bout 10 years ago, pretty girl comes in with a specific list of kit, pc/pouches etc, when asked where she played she replied "oh no they're not for me, my fiances deployed in Afghanistan & his issued kit is shit, literally rotting off him in the conditions, so I need to post these to him asap"
I was disgusted then, still am tbh, if my son turned round & said he wanted to join up, id slap that shit out of him, irrespective of the fact I served, different times & different agendas.