Why should tenants be paying more than inflation? Well, for a start, it depends what you mean by inflation. The RPI figure is pretty unrepresentative, as it includes mortgage interest payments.
There are better measures of general price inflation (e.g. RPIX, which excludes mortgage payments, or CPI, which is more up-to-date and used by the Bank of England as an inflation target). CPI is still rising at over 2% a year.
The only people who are experiencing price deflation are homeowners with floating-rate mortgages: a lucky few. For the rest of us, prices are still going up, in case you hadn't noticed.
There's an argument that since RSLs borrow against property their costs are more likely to follow the RPI trend (i.e. benefiting from falling interest rates). However, most RSLs have a sizeable proportion of their borrowing at fixed rates, and the new rates charged by lenders haven't fallen nearly as much as the Bank of England rate, so RSLs aren't benefiting from cost deflation as much as the RPI figures might suggest.
RPI is still used as an inflation measure for all sorts of things aside from rent (e.g. pay deals, rail fare increases). For a long time it suited a lot of people (employees, pensioners and thus politicians) to keep RPI as the measure rather than switch to CPI, as RPI had always been higher than CPI. The boot's on the other foot now.