No, not all the variants in the browsers produced by the 1000 Genomes Project were discovered by the 1000 Genomes Project.
The data from the 1000 Genomes Project is available in a number of browsers, including browsers produced by the 1000 Genomes Project, which reflect the major data releases associated with the pilot, phase 1 and phase 3 publications from the 1000 Genomes Project. More information on this is available on the browsers page.
The content of the 1000 Genomes Project Browsers, maintained during the 1000 Genomes Project, are based on custom versions of the Ensembl browser. These databases contain the Ensembl core features (genes and transcripts), regulatory elements from the Ensembl Regulatory Build and variation data from the Ensembl Variation database.
As well as 1000 Genomes Project variation data, Ensembl variation contains data from dbSNP, ClinVar, COSMIC, dbGaP, dbVAR, EGA and many other sources.
Ensembl and UCSC Genome Browser both import their variant data from dbSNP. When new 1000 Genomes variants have been released it can take some time for them to be accessioned by dbSNP and make their way to the browsers.
When this happens we try to ensure there is a version of our own browser which displays the data in the meantime. Both Ensembl and UCSC support attaching VCF files to them for visualisation