this is not true, it is still "freedom of movement (for workers)"
the granny example is explicitly not permitted unless they have sufficient funds to support themselves without the target states' assistance (meaning independently wealthy)
you can be deported otherwise
This is totally wrong.
The granny can get her pension anywhere in the EU, no "independent wealth" required.
There are some restrictions if you have no means to support yourself and require benefits, but the restrictions are definitely not as broad as "granny needs much money on her bank account"
Read: https://commission.europa.eu/strategy-and-policy/policies/ju... and links contained therein
your linked page alludes to this, without details
> In order to stay in another EU country for more than three months, EU citizens have to meet certain conditions depending on their status (for example worker, self-employed, student, etc.) and may be asked to comply with administrative formalities.
if you follow the wizard on your page you get this:
https://europa.eu/youreurope/citizens/residence/residence-ri...
(Just curious; I know this is a tangent!)
The 65 year old would need to live from their pension for a couple more years.