This is absolutely true, and to an extent that is hardly believable to most modern folk. The population explosion in New York City during the 1840s and 50s was a big part of this, for it radically altered the social landscape of the city, and created ethnic enclaves that became vital for politicians looking to secure positions from alderman to mayor. Although deals have always been a cornerstone of politics, in any country, New York City's unique position as a veritable melting pot for Irish, English, German, and Italian immigrants helped foster very rigid lines of sectional loyalty. These immigrant groups often had community bosses or figureheads that could promise huge swaths of votes in exchange for political appointments, state contracts, land deals (favorable to one particular bidder, despite the size of their offer), and the like. This meant that to get anything done, or to have any deal pushed through, a politician had to be tied in with one or many different factions that intermingled between social, political, or even religious lines.

As a result, in New York during the 2nd half of the 19th century, EVERYONE was tied into some level of corruption, graft, or political influence. The fire department, police, state senators, assemblymen, the mayor's office: everyone was getting a cut, and were greasing wheels (or themselves getting greased).

Any history on Boss Tweed and Tammany Hall would be a great start for you if you wanted to research this further. I might recommend Ken Ackerman's book 'Boss Tweed' or perhaps Daniel Czitrom's 'Underworlds and Underdogs'