I can think of two specific instances of people who essentially paid for large chunks of their houses by relatively generous relocation packages, in one case, they didn't actually move house - this was the sort of deal where he had to work further from home, so could have relocated, but decided to just commute a long way and was told he could have the money anyway. In neither case is there any suggestion of deceit / impropriety / kickbacks / whatever, this is just how things were done. I can think of two cases where I know all of the details, but I have heard of lots of similar things over the years, it is just how things were done. I think things began to change in the mid-80s - indeed at my second job I got 2 months B&B / cheap hotel accommodation paid for or could have had moving / conveyance costs if I'd owned a house, whereas people who joined a year before at the same grade got 6 months accommodation paid for AND moving / conveyance costs.
The 'I have paid off my mortgage so can claim less money, but since I could have not paid it off and got more, can I have that larger amount instead' incident sounds to me exactly the sort of thing that would have been nodded through, I do remember something vaguely similar happening.
The issue, really, therefore, is not that this is all ludicrous dishonesty, but that the way the scheme works for MPs harks back 25-30 years to a more generous age.
I am not saying that this makes it much better, but I think it does make some of the hue and cry rather intellectually dishonest.