Yes, and that's a big part of the problem, which is why tiktok is also under fire in this whole situation.
An obvious hack to bypass this is to assemble "a group of citizens" who start spending money to campaign for a candidate without any direct connection to them, but in such case, there's a special commission run by retired campaign finance people that analyzes the spending and can take action like demand a candidate to pay back over-cap portion of the money spent to advertise them, even if someone else paid for it. In the worst case, this can be escalated to the Supreme Court, who has the authority to scrap and re-run entire elections if the impact of illegal practices is deemed large enough to sway elections.
So far, this system has produced a very transparent campaign financing environment. It was heavily tested in the first few years and withstood attacks remarkably well. A shadow figure of a political party used a retail network they owned to run a huge advertising campaign for a keychain that depicted the mascot of a major political party in their colors. The party was never directly mentioned, but you were blasted everywhere with their colors and the same animal as their mascot. After years of legal battles, it was deemed an illegal donation and the party had to pay for it all back with penalties. It was such a financial blow that the party underperformed for the next few electoral cycles due to constrained finances. No-one dares to try these tricks since then. Both financially and politically, it's cheaper to respect the rules.
Anyone can buy ads and flyers.
If your rejoinder is "It's against the law to buy ads for a candidate if you're not officially part of the campaign" - who cares? Nothing is stopping e.g. me from buying tiktok ads in elections (domestic or foreign).