In both scenarios the pitfalls exist. Typically a user who uses the net will mostly have the following running on his machine. Instant Messengers(yahoo, MSN), a web browser and might use a FTP client. If all other services are shut off then a prospective cracker will look to hack into these services. Plus many tracking services use your IP addresses to track your activity online. Lets say "unwanted" sites
. If I use a anonymous proxy server then tracking it to my end IP is usually extremely difficult. However if you do use an Anon-proxy and I am crazy enough to login to my emails well ur asking for trouble arent u
Both has its pro's and cons. And as you correctly mentioned the reason as to why he wishes to remain anonymous has not been mentioned by the user!!!!!