It's absolutely possible to get customers / clients without doing any paid advertising.
As you suggested - this can be from word of mouth or from a variety of other sources.
Effective marketing plans often utilize a broad spectrum of both inbound and outbound strategies. And some business models lend themselves incredibly well to methods that involve little or no money. Other strategies / techniques / platforms require a bigger investment. (Notice I used the word "investment" not "spending")

In my opinion, the key is to create a business model that allows you to maximize your return on investment (ROI) for all of your marketing (and quite frankly just ALL) dollars.

For guidance on how to create such a business model - give me a call.

In all likelihood, these folks are defining "advertising" as paid promotional efforts. With so many tools at our disposal for doing organic (non-paid) marketing, many companies are able to get off the ground and start seeing success by focusing their efforts on these organic channels (email marketing, blogging, SEO, social media, website optimization, lead nurturing, etc).

By leveraging these inbound marketing channels, building out a strong content strategy, and developing a strong and diversified online presence, you should be able to get your business in front of many new audiences, without having to pay for banner ad placements and Adwords campaigns.

As the manager of the paid marketing channel for an inbound marketing company, one of my most important endeavors is finding ways to scale back our advertising spend and help increase our yield of new leads and customers from our organic channels. I'd be happy to discuss organic vs. paid strategy with you greater detail if you want to hop on a call.

David brings up a great point. You are INVESTING in something -- relationships, great design, strategy, content, etc...

There is no such thing as a 'FREE' customer. You have to spend money to land that customer. You might spend that money on advertising or on a better content marketing team.

Don't expect big results with little investment. It's going to cost you.

Every competitor tries to dominate the market and show that they are different from the rest so that their products get an advantage over yours or for that matter any other in the market. Do not be fooled by it. Even if they are not saying it directly to you, they are doing it. All they are doing is trying to market out as many competitors as possible nothing else with these comments. No body can survive without any advertising. For to stay on-the-top of customer list you need to advertise.
Depending upon the nature of your business, staying in contact with your customers can help generate referrals by keeping your name top-of-mind. Many personal services businesses, such as accountants and real estate agents, send birthday and holiday cards to their customers. Other businesses, such as hair salons, offer discounts or a gift certificate to customers who provide a referral that brings in new customers. Printed material includes items such business cards, letterhead, brochures, flyers, gift certificates. Brochures allow you to provide enticing details about your product or service. Simple three-fold brochure paper may be purchased from mail order suppliers such as Paper Direct. Give your customer as much quality information as you can pack into this identity piece.
You can read more here: https://www.bizfilings.com/toolkit/research-topics/marketing/advertising-pr/effective-advertising-makes-people-remember-your-name
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath