You sort of answered the question yourself "a company's right... to block".
Companies may do such "blocking" of internet or email access for multiple reasons, such being that sites could contain bad code that could present risks to their system (whether they have firewalls or A/V or whether such is up to date). Workers accessing their personal email at work could put the business system at risk, again due to emails containing bad code. Similar, if a worker sent and email through their own private domain or private email account, that sent email could also contain the IP of the company. The recipient could consider that email spam and the company's IP could get onto a blocked list.
Yes, many reasons why a company may restrict access to the internet by the workers, and mpst definitely a right of the company and for some it may be a necessity to maintain security.
It is also one way that a company can ensure that a worker is not doing other non-work things during business hours. As for the workers lunch time or other breaks, the worker should simply not be using the company equipment for their own personal usage... the company owns the equipment. (Maybe if the worker paid for "rental time" and a share of a/v software costs.... to compensate the employer....)
If it is a sports site or even a business site that interests people and workers then, in my opinion, the persons should use their own computers at their own home and on their own time.
Rather than trying to circumvent "controls" that employers may have on their systems, time might be better spent trying to improve site functions, features, speed and other items on such a site. Not every person has high speed access at home, many still use 56k dialup, so a site owner should make sure that their site is not slow at 56k and that it does not contain a lot of garbage, such as pop-ups or too many ads (and of course I personally think that shockwave or similar movies are wasteful of time... the plugin I removed... usually any content in such can be displayed via jpg, gif, animated gif, or other means).
Also, if one has a business site and wants to capture more viewers or clients, extended "help hours" or later business or customer service hours (even to accomodate east/west coast time differences) can make a big difference.
Otherwise I don't have any suggestions how you could circumvent controls imposed by a company. I would guess that they have automated software performing most of the restrictions, and if not, then they would have IT staff who would easily notice any non-business activity and would put a stop to it.
My best suggestion would be just to make your site the best that you can and hope that it's content is what users want and that they will come to your site during their own personal time at home.