This is false. The calls would already be discounted by the dividend prior to x-div.
As I write this, 1,200 $70 August 18 calls for HCN are being visibly offered for $2.35 while the stock is trading at $71.83, a premium of $0.52, which is, importantly for this example, less than the recent $0.87 dividend.
In reality, stock prices have fluctuated as usual for the past two days, but had the stock price remained completely constant since the day before it went ex-dividend, and adding in the dividend for the pre-dividend price, it would have been trading before the dividend at $72.70. If, at that time, "the calls would already be discounted by the dividend prior to x-div", the $70 call should have already been available for today's asking price of $2.35 plus a little more to back out the theta decay, so, let's say $2.40. If that were true, you could have gotten filled on combination orders to buy the $70 call at $2.40 and short the stock at $72.70, then exercised the call for an immediate profit of $0.30 per share minus commissions, and you could have repeated the process many times throughout the day, making a fortune, or maybe just $36,000 minus commissions if those 1,200 contracts were the only ones on offer.
I believe option sellers are, in reality, not so stupid to make such offers before the ex-dividend date.
I encourage you to look for examples by watching the dividend calendar at
http://www.nasdaq.com/dividend-stocks/dividend-calendar.aspx . Keep in mind that today is a somewhat bad day to look for examples, as most of these stocks only have options that expire on the third Friday of the month, which is still two weeks away, and the market has had some news to digest over the past 24 hours (grand jury rumors then surprisingly good economic data), so it is harder to find examples this morning where option premiums are really low. My point should be easier to see if you look at very stable stocks going ex-dividend closer to options expiration day, ideally when there is relatively little economic news.