That’s not true, for two reasons.
(1) Most brokers are market-makers, meaning that they set their own BID and ASK prices based on the best available prices offered to them by their liquidity providers. Two brokers in distant parts of the world may be getting their (wholesale) prices from different groups of liquidity providers (banks). Accordingly, at any given moment, the best BID and the best ASK available to broker #1 might be different from the best BID and ASK available to broker #2.
Then, being market-makers, these two brokers will create retail BID and ASK prices, which they will offer to you (the retail customer), by marking-up the wholesale BID and ASK prices from the bank. This marking-up involves subtracting pips (or fractions of a pip) from the wholesale BID price, and adding pips (or fractions of a pip) to the wholesale ASK price. These mark-ups represent profit for the brokers, and typically vary widely from broker to broker.
All the prices you see on a broker’s platform (including the daily opening and closing prices) are marked-up retail prices. Different prices displayed by different brokers are the result of different mark-ups.
One more point: Charts display either BID prices or ASK prices, as determined by the user of the charts. When comparing prices between brokers, be sure to compare BID price to BID price, or ASK price to ASK price.
(2) Each broker decides for itself when the “forex day” will end, and a new “forex day” will begin. The time chosen may or may not match the time chosen by another broker. Many (but, not all) brokers use the end of the business day in New York (5 pm New York time, 9 pm or 10 pm GMT depending on daylight saving time in New York) as the “close” of the forex trading “day”. But, other brokers use other times, such as midnight local time, or midnight GMT, as the time at which they close one daily candle and open the next daily candle.
Obviously, opening and closing daily candles at different times of day will result in different opening and closing prices.
Some additional time-frame info
All brokers worldwide open and close hourly candles at exactly the same time. As a result, the candles on all the smaller time-frames (30-minute and lower) open and close at exactly the same time, as well.
But, on time-frames from 2 hours to 12 hours, candles are synchronized with the broker’s daily candle closing time. Example: a broker that closes daily candles at 5 pm New York time will close 4-hour candles at 5 pm, 9 pm, 1 am, 5 am, 9 am, and 1 pm. But, a broker that closes daily candles 2 hours later, at midnight GMT, will close all of their 4-hour candles 2 hours later, as well.
All brokers, regardless of where they are located, open and close weekly and monthly candles at exactly the same time. But the prices displayed on those candles may differ from broker to broker for the reasons discussed in (1) above.
One of the challenges in trading a worldwide market is that languages, customs, regulations and times vary from place to place. As for times, as you go around the globe, there are 24 hourly time-zones plus several half-hourly time-zones. It’s essential for a trader to know his broker’s time-zone (meaning, generally, where the broker’s servers are located). All of the times displayed on that broker’s charts will be based on that time-zone.