Each ticket is an independent event, yes.
1:300,000 is an independent event.
Another 1:300,000 is an independent event.
Together they give you a 1:150,000 chance of hitting a prize that has 1:300,000 odds on a single ticket.
Edit: In case I can make this even clearer, two tickets that each give you a 1:300,000 chance give you a 2:300,000 chance when put together.
Well, I suppose if you bought all 300,000 tickets you could guarantee that you'd win your $25,000 jackpot.
What people are trying to explain to you is that you can expect your return on investment, as a percentage of the amount you spend on lottery, to be the same whether you buy 10 tickets or 1,000 tickets.