Yes they can legally do it. They can't prevent the club receiving the money as that would be restriction of trade. That's not what they're saying they'll do though. They can though say that for the purposes of the FFP rules they won't count certain transaction types. For example they're choosing to exclude spending on the youth system and other capital investments. If they decide that funds received from related companies will be excluded from income for the purposes of their calculations there is nothing illegal about fining the club for not meeting the criteria that as members of the FL they have agreed to be bound by. It's no different to tax accounting being done differently to the financial accounting that gets reported.
Man City have proved nothing as the rules have only just come into play this coming season. They have also been warned by UEFA that they are at risk.