XMLHttpRequest is not designed to be used in a streaming fashion. As long as the server sends more data, the browser will continue appending it to the responseText
field in the XHR object.
Therefore, I'm pretty sure that what they meant is that the JS code using XHR for streaming would have to periodically drop the connection and open a new one — or else leak memory due to keeping all data ever received, as well as wasting time reallocating a forever-growing string.
That is, the limitation is one you must implement in order to have acceptable long-run performance, not one imposed by the browser. (There may well be also a browser-imposed cap on response size, but I don't know if there is.)