The player's betting history says that the only two things he could be guilty of is multi-accounting or bot use. The player had a small limit in a small market and made max bets. The odds provider just profiled the player based on his betting history and set his limit. There's no need to get the odds provider involved unless there's a claim of a bad line. The book needs to prove bot betting or multi-accounting.
In the case of arbitrage betting for a sportsbook it's not possible to know if the player is arbitraging especially if he is using more than one betting platform. But the sports provider can detect it easily when the same player is using more than one sportsbook that they are working as provider.
Let's understand an example. Sportsbook A, B and C can have same sportsbook provider. A players is using all these sportsbook to bet in win - lose - win market to benefit from the odd. Individual sportsbook will have no data of what is happening in other two sportsbook but the provider can see all data together and easily can detect the player is benefiting from arbitrage betting. The provider flag the player and order all three sportsbook to ban the user from their platforms. Sportsbook have to accept it if they want to stay with the same provider.