Repulogy

Absolutely not. You will notice that our process always gives the customer the option to leave a third party review, whether they are happy or not.

There are three main reasons for this:

It's not hard for your customers to notice when you're taking their happy reviews publicly and negative reviews internally. Using these methods will cause your customers to trust you less, and your unhappy customers will inevitably find a way to get their voices heard anyway.
It breaks the terms and conditions of most review sites out there, so can lead to problems for your review profile in the future. All it takes is one of your customers reporting your practices to the review sites, and you risk your profile being banned.
Unhappy feedback is only natural for any business, and it makes you look real. In this sense, potential customers will be looking at how you respond to that feedback than anything.