Is it true that the barcode indicates the country of origin?

No that's not true. In retail stores in England, for example, you will find products from a Canadian manufacturer, but with a barcode from a Spanish distributor with an barcode originally issued in Greece. The EAN system is designed for this type of retail activity.

Because any participant in the retail process can take responsibility for obtaining barcodes for a product - the company that came up with the product or the manufacturer, or the importer, distributor, or even the retailer himself! And these participants in this process can be located not only in different countries, but even in different continents. And it is natural that the barcode cannot indicate the country of the manufacturer in any way.

Quote from GS1:

«Note that since GS1 member companies can manufacture products anywhere in the world, GS1 prefixes do not identify the country of origin for a given product».