Tansport bills if fake can be checked into by making it compulsory to give 3 different quotations from 3 different transporters and then finalzing on the feaseable one.
Regarding Medical Bills, if its a genuine Medical Store Bill (of course bill number, doctor name, CST, VAT Details etc.), then I think one should not dwell deep into it. Just Pay out the re-imbursement afterall these costs are included in the CTC. The logic used is that if an employee visits a doctor or specialist for treatment then the company doesnt pay for it ...so what is the harm if it reimbuses genuine bills as per norms no matter how the employee has got it. The onus of issuing such bills lies on the medical store afterall. HR doesnt need to be a CBI in everything I guess. There are people higher up the ladder in Management who litterally flout the rules for huge sums (petrol bills, mobile, clothing etc.) wherein nobody questions. It would lead to Penny wise and Pound foolish kind of scenario. If you start pinching mid-level employees everywhere, you will create the road towards your own downfall. Look at what has happened to Satyam!!!!!!!!
Obviously this is just my thoughts which i implement and maybe someone else might differ on this.