The question (and it’s a good one) isn’t why Hank the DEA agent needed Walter to pay his medical bills. The question is why Hank would have needed Walt to pay his medical bills if everything else in Walt’s confession was true. The way Walt tells it on the tape, Hank built a meth empire, and “sold [Walt] into servitude,” making meth for Gus Fring. If that’s the case, then it would seem that Hank would have made as much, if not significantly more, money than Walt - so, why would Hank have needed Walt to pay the bills?
Money laundering. If Hank is the king pin he’s doing a good job of living within his means and not drawing attention, so where ever he has the money it’s not readily accessed. Now he’s got medical bills that he can’t “afford” to pay with his documented income. The fix for that is having his relative, whose “additional” income has been laundered to some extent, pay. Keeps everything nice and explicable, just the way the IRS and IA like it.
It is a good question. Maybe Hank was laundering all the operation’s cash through the White’s carwash, which he made Walt set up, especially for that purpose? The cover story about Walt’s ‘gambling addiction money’ works just as well for a ‘badguy’ Hank as it does Walt, I suppose. If Hank told any of his buds at work about his crazy brother in law Walt’s supposed addiction, it would look like Hank was making it up out of whole cloth as a way to cover the cash injection?
Freegards
I suspect that whatever else happens between Hank and Walt, it won't be official DEA business.
Hank could not pay the bills because it would expose him to the DEA as someone with way too many assets. These folks have a nice pension and god salary, but most live month to month.
Their medical insurance is all they got.