I can't comment on the difference between the web and console environments, but the problem Harry's referring to should only affect free account holders. Let me try to explain a little about the setup which will hopefully show why this is only a problem for free accounts, and explain the reasons for it. I should point out this is based on my own understanding and I'm not a PA dev - I'm just another user.
The problem is that free accounts are easily open to abuse, because there's nothing to stop someone registering quite a few different free accounts and using them to either attack or spam other websites and services. As a result, PA implements firewall rules which prevents outgoing TCP connections - this includes websites, email, SSH, everything.
Since it's useful to be able to make requests of certain sites, however, there is a proxy server supplied for free accounts which allows access to any website on the whitelist. This proxy server is specifically allowed in the firewall rules, so you can connect to it and then make requests of websites via it. Typically this is totally transparent as most HTTP libraries in Python will automatically make use of the proxy without any explicit configuration.
Email is therefore typically blocked, but since it's such a useful function there's another exemption in the firewall rules for Google's mail servers to allow sending of email via a Gmail account. Unfortunately this exemption is added via IP address and Google have a habit of changing their IP addresses frequently. The PA system attempts to keep the firewall up to date, but there's often some delay between Gmail changing the addresses and the PA system updating their firewall rules - this is because it's a complicated distributed system and it takes some time for these changes to take effect. This isn't a failing in a core PA service, it's just a difficulty of allowing access to Gmail's servers in a secure fashion, which is provided on a best-effort basis.
Paid accounts, on the other hand, don't suffer any of these restrictions - they can freely make outgoing requests to external sites, for HTTP, email or anything else. The firewall updates aren't an issue because there are no firewall rules. The proxy isn't an issue because you don't need to use the proxy. PA can afford to do this because paid accounts are much less open to abuse - if someone abuses other sites via PA, the devs have a lot more potential to block that user in the future than on a free account. They would, of course, only do this for genuine abuse such as DoS attacks on other sites.
I should also add that there's a 30 day no-quibble money-back guarantee on account upgrades - if you decide the service doesn't meet your needs within 30 days of upgrading, you can get a full refund on the first month's subscription.
Whether you upgrade is of course up to you, but hopefully that's explained how and why there are much fewer restrictions on paid accounts.