Well, it depends on how disfunctional your country is, but generally that's not true:
https://www.eea.europa.eu/ims/waste-recycling-in-europe
And in the US per-state:
https://www.eunomia.co.uk/reports-tools/the-50-states-of-rec...
> The study ranked each state according to its recycling rate for CCPMs in 2018, with the 10 states with the best recycling rates comprising: Maine (72%); Vermont (62%); Massachusetts (55%); Oregon (55%); Connecticut (52%); New York (51%); Minnesota (49%); Michigan (48%); New Jersey (46%); and Iowa (44%).
Note for comparison purposes, that US report is on CCPM (plastic bottles and trays, glass bottles and jars, aluminium cans, steel cans and cardboard and boxboard), which the EU calls out seperately as "packaging waste" with an average of 66%.
And it's 'material reprocessed rather than material collected for recycling' they count.
That recent Greenpeace USA study suggests that only type 1 and 2 plastics are close to meeting their 'actually being recycled into more of the same stuff' targets across the USA.