In most they are limited to a very high number. You will run into performance constraints far earlier than reaching any set limit on the number of records in a database. Your limit in just about every case is the hardware that the database is running on, and the actual design of the database and the application accessing it.
They are right there is no limit. Currently I have website that uses a sql database with 1,085,623 rows.
For record in SQL Server is growth follow your insertion record, it no have limit. Currently on 4 million record make the processing more slow than below that number.