Can lightning strike a player on the field in a sports stadium...

Your explanation has not offered any evidence that a player’s safety is “much much better” somewhere else within the venue, than on the pitch. Only that if the lightning strikes, there is no safe place where one can have a high assurance of being unaffected by it. Unless you can offer statistical or scientific evidence that a player on the pitch is more likely to be struck than one huddling inside the structure near electrical wiring and steel support beams and high-conductivity materials and amenities, let the game go on.,

You’re comfortable making this determination for other people?

Do we have a firm number X%? No. If that’s not sufficient for you, then you can establish that as the rule for your league or for yourself. Besides, what you consider safe or not for other people veers into GD territory.

At any rate, many sports organizations have already set safety rules for the presence of lightning or thunder. So, again, in response to the original question and the only real GQ response, the players were not being unreasonable in asking to take their own safety into consideration as this is a usual and customary practice in most if not all professional sports, and this practice is based on a known elevated risk of injury, even if the precise amount of risk elevation is not known to the Nth decimal place.

I read your explanation (not that of other people) and I found no evidence within it that one part of the venue is safer than another. That standing on the pitch is more dangerous than standing next to an electric vending machine in the concourse. Maybe it is, but you haven’t defended the proposition.

http://usatoday30.usatoday.com/weather/storms/2005-10-06-lightning-football-player_x.htm

In Florida and most other states, high school football games happen at night, so this field was certainly surrounded by light towers.

http://www.crh.noaa.gov/pub/?n=/ltg/ncaa_ltg.php

Note the times in these examples.