i need to draw a diagram to exmplain it really.
your device connects to the blackberry.net GPRS APN (which goes via the provider, but still conencts directly to BLACKBERRY's network) ie the data travels through a tunnel to blackberry doesnt really touch the prover directly
your BES server connects to the blackberry.net main mail server via the internet (again, kinda transparently touching the internet ISP)
also if you're on lotus notes then yes you'll need blackberry coz activesync is exchange only
ps notes is shit
also there's a new thing called blackberry connect, which is blackberry client software for your PDA/smartphone.
you can get blackberry on your XDA2 or Nokia 9300 of palmOS PDA etc. etc. it doesnt support as many features as a "proper" blackberry handheld tho (but proper blackberrys are shit imho

)