Beijinghua is not Putonghua
Many Mandarin learners think that Beijinghua (北京话) is Putonghua (普通话), in fact, not only Putonghua, but the best Putonghua. For this reason, they seek Chinese teachers who are originally from Beijing, or they believe that they should go to Beijing to learn Putonghua.
My personal experience
I grew up in a small city in Hebei (河北), and Beijing is 30 minutes away by car or 60 minutes by train. I always thought it was great to live in a place so close to the capital.
As the capital of the country, Beijing has a lot to offer. We always found good reasons to go there. I made countless trips to Beijing, class tours, family trips or friends getaways. We visited museums, parks, and many historic sites. We also talked to many people who grew up in Beijing.
When I spoke to Beijing people, I always felt we spoke quite differently. Sometimes I tried to mimic them, such as how they swallowed up lots of sounds and the words I only heard in Beijing.
This experience tells me that Beijinghua is NOT Putonghua. They are very closely related, but definitely not the same.
My conclusion is confirmed by linguistic experts on a theoretical level, that Beijinghua is really not Putonghua.
According to linguists, Beijinghua was heavily influenced by Manchu language.
At the beginning of the Qing Dynasty (1644 - 1912CE), when Manchu people came to Beijing to rule, they began to learn Chinese. Their Chinese accent was influenced by their first language.
Gradually, Beijinghua emerged. It is a version of Chinese language integrated with some aspects of Manchu language and is filled with a massive amount of neutral tone words. Moreover, like other dialects, Beijinghua is full of its very own colloquial and slangs which don't exist anywhere else.
For people who did not grow up in the Beijing area, they have difficulties understanding those colloquial and slangs.
Different versions of Putonghua
In the 20th century, the Chinese government started promoting Standard Mandarin Chinese (Putonghua).
Putonghua is based on Beijinghua, but it did not adopt Beijinghua completely. Therefore, if students have been learning standard Mandarin Chinese (Putonghua), they will find it challenging to fully understand Beijinghua.
It is very interesting to know that a similar scenario, but in much smaller scale, also happened to Cantonese (广东话) and Hakka (客家话), and Shanghaihua (上海话) and Ningbohua (宁波话).
For the same reason, people who learned Cantonese find it challenging to understand Hakka, and people who learned Shanghaihua find it difficult to understand Ningbohua.
Local dialects have great influence on teaching and learning Putonghua.
If students are learning Putonghua in Beijing, their Putonghua will be influenced by Beijinghua. If students are learning Putonghua in Guangzhou, their Putonghua might be affected by Cantonese.
There are so many dialects of Chinese. There are probably many versions of Putonghua. This diversification of Putonghua can make my imagination run wild. There could be hundreds versions of Putonghua out there with slight differences from one another. Not only it is possible to speak Putonghua with a Chinese southern accent or a northern accent, but also speaking Putonghua with Italian accent, Thai accent or Portuguese accent!
Fortunately, Putonghua, despite the influences of the local dialects, is common enough to enable people to understand each other no matter where they have learned their Putonghua, or what their mother tongue is.
That makes learning Putonghua interesting. Everywhere could be a good place to learn. Hong Kong is no exception. Despite a few disadvantages, it is a fabulous place to learn Putonghua. Many students have had the time of their lives while learning Mandarin in Hong Kong.