Transport bills, if fake, can be checked by making it compulsory to provide 3 different quotations from 3 different transporters and then finalizing on the feasible one.
Regarding Medical Bills, if it's a genuine Medical Store Bill (including bill number, doctor's name, CST, VAT details, etc.), then one should not delve too deeply into it. Simply reimburse the cost as these expenses are already included in the CTC. The rationale is that if an employee seeks medical treatment, the company does not cover the expenses. Therefore, reimbursing genuine bills according to norms, regardless of how they were obtained, should not be problematic. The responsibility of issuing such bills lies with the medical store. HR does not need to investigate everything like the CBI. There are individuals in higher management positions who blatantly violate rules for significant amounts (e.g., petrol bills, mobile expenses, clothing, etc.) without being questioned. This could result in a situation where being overly cautious about small expenses leads to larger losses. If you scrutinize mid-level employees in every aspect, it may pave the way for your own downfall. Consider what happened to Satyam!!!
These are simply my thoughts that I implement, and others may have differing opinions.