Unfortunately, this is entirely correct and an important issue to flag up when choosing a savings account.
Banks and building societies often change the interest rates available on accounts, without changing the account name, so it is possible for the exact same account to pay different interest rates to different people.
This happens because the providers quite often push up their rates on a short-term basis to lure in new customers, leaving existing customers on lower-paying rates.
But as the name of the account stays the same, this practice can be hard to spot. For example, savers with the Halifax ISA, which was launched last year, could be earning 2.6%, 2.75% or 3% depending on when the account was opened.
This doesn't just apply to tax-free ISA accounts either.
The Sainsbury's Extra Saver account pays between 2.5% and 2.75% and the Nationwide MySave Online Plus deal pays between 1.5% and 3.17% depending on when you opened it.
It's also worth watching out for bonus rates. The Halifax account you mention has a hefty bonus of 2.5% added for the first 12 months so after this point the interest will plummet.
The best way to combat this is to read all the small print first. Before signing up to an account, shop around and check other rates, and don't stick to one provider as you're much more likely to get a better deal on a short-term account by regularly swapping accounts rather than being a loyal customer.